##############ECHO OF PROBLEM################# ##############temp/mtest6postode.ode################# diff ( x1 , t , 1 ) = 4.0 * x2 - 2.0 * diff ( x2 , t , 1 ) - 2.0 * x1 ; diff ( x2 , t , 2 ) = 3.0 * diff ( x2 , t , 1 ) - 2.0 * x2 - diff ( x1 , t , 2 ) - diff ( x1 , t , 1 ) + x1 ; ! #BEGIN FIRST INPUT BLOCK # Digits:=64; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb t_start=1.5 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb t_end=8.0 $array_x1_init[0 + 1] = exact_soln_x1(t_start) # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $array_x2_init[0 + 1] = exact_soln_x2(t_start) $array_x2_init[1 + 1] = exact_soln_x2p(t_start) $glob_look_poles=true $glob_max_h=0.0001 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=0 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=16 $glob_max_minutes=3.0 $glob_subiter_method=3 $glob_max_iter=100000000 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_x1 (t) c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return(2.0 * c1 + 6.0 * c3 * exp(-t)) end def exact_soln_x1p (t) c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return( - 6.0 * c3 * exp(-t)) end def exact_soln_x2 (t) c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return(c1 + c2 * exp(2.0 * t) + c3 * exp(-t)) end def exact_soln_x2p (t) c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return( 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 6.5 estimated_steps 6500000.0 step_error 9.8058067569092e-22 est_needed_step_err 9.8058067569092e-22 opt_iter 1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 2.0004016342882673 min_size 1.0040840464326821 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 1.0040840464326821 desired_abs_gbl_error 1.004084046432682e-16 range 6.5 estimated_steps 6500000.0 step_error 9.845854127014326e-22 est_needed_step_err 9.845854127014326e-22 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.900103781919588e-250 estimated_step_error 7.900103781919588e-250 Double H and LOOP opt_iter 2 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 2.0004016342882673 min_size 1.0040840464326821 $glob_desired_digits_correct 16 estimated_h 2.0e-06 estimated_answer 1.0040840464326821 desired_abs_gbl_error 1.004084046432682e-16 range 6.5 estimated_steps 3250000.0 step_error 1.392414043957077e-21 est_needed_step_err 1.392414043957077e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.428910127263391e-239 estimated_step_error 5.428910127263391e-239 Double H and LOOP opt_iter 3 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 2.0004016342882673 min_size 1.0040840464326821 $glob_desired_digits_correct 16 estimated_h 4.0e-06 estimated_answer 1.0040840464326821 desired_abs_gbl_error 1.004084046432682e-16 range 6.5 estimated_steps 1625000.0 step_error 1.9691708254028652e-21 est_needed_step_err 1.9691708254028652e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.730718833583601e-228 estimated_step_error 3.730718833583601e-228 Double H and LOOP opt_iter 4 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 2.0004016342882673 min_size 1.0040840464326821 $glob_desired_digits_correct 16 estimated_h 8.0e-06 estimated_answer 1.0040840464326821 desired_abs_gbl_error 1.004084046432682e-16 range 6.5 estimated_steps 812500.0 step_error 2.784828087914154e-21 est_needed_step_err 2.784828087914154e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.5637307380901613e-217 estimated_step_error 2.5637307380901613e-217 Double H and LOOP opt_iter 5 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 2.0004016342882673 min_size 1.0040840464326821 $glob_desired_digits_correct 16 estimated_h 1.6e-05 estimated_answer 1.0040840464326821 desired_abs_gbl_error 1.004084046432682e-16 range 6.5 estimated_steps 406250.0 step_error 3.9383416508057304e-21 est_needed_step_err 3.9383416508057304e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.761782729061621e-206 estimated_step_error 1.761782729061621e-206 Double H and LOOP opt_iter 6 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 2.0004016342882673 min_size 1.0040840464326821 $glob_desired_digits_correct 16 estimated_h 3.2e-05 estimated_answer 1.0040840464326821 desired_abs_gbl_error 1.004084046432682e-16 range 6.5 estimated_steps 203125.0 step_error 5.569656175828308e-21 est_needed_step_err 5.569656175828308e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.210688396177503e-195 estimated_step_error 1.210688396177503e-195 Double H and LOOP opt_iter 7 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size 2.0004016342882673 min_size 1.0040840464326821 $glob_desired_digits_correct 16 estimated_h 6.4e-05 estimated_answer 1.0040840464326821 desired_abs_gbl_error 1.004084046432682e-16 range 6.5 estimated_steps 101562.5 step_error 7.876683301611461e-21 est_needed_step_err 7.876683301611461e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.319794503070188e-185 estimated_step_error 8.319794503070188e-185 Double H and LOOP opt_iter 8 SETTING H FOR MAX H NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 START of Soultion TOP MAIN SOLVE Loop t[1] 1.5 x1[1] (closed_form) 2.0004016342882673 x1[1] (numeric) 2.0004016342882673 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.0001 x2[1] (closed_form) 1.0040840464326821 x2[1] (numeric) 1.0040840464326821 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 1.599999999999989 x1[1] (closed_form) 2.0003634137323902 x1[1] (numeric) 2.0003593940414417 absolute error 4.019690948542376e-06 relative error 0.00020094803378963082% Desired digits 16 Estimated correct digits 12 Correct digits 6 h 0.0001 x2[1] (closed_form) 1.00496707499482 x2[1] (numeric) 1.0049693666766857 absolute error 2.2916818656071314e-06 relative error 0.00022803551704606278% Desired digits 16 Estimated correct digits 12 Correct digits 6 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 1.699999999999978 x1[1] (closed_form) 2.000328830343295 x1[1] (numeric) 2.000312711349069 absolute error 1.6118994226044236e-05 relative error 0.0008058172227252209% Desired digits 16 Estimated correct digits 11 Correct digits 6 h 0.0001 x2[1] (closed_form) 1.006047625066695 x2[1] (numeric) 1.0060580637569914 absolute error 1.0438690296377118e-05 relative error 0.0010375940498527686% Desired digits 16 Estimated correct digits 11 Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 1.799999999999967 x1[1] (closed_form) 2.000297537998799 x1[1] (numeric) 2.0002611189950867 absolute error 3.641900371231799e-05 relative error 0.0018206793249744956% Desired digits 16 Estimated correct digits 11 Correct digits 5 h 0.0001 x2[1] (closed_form) 1.0073692365552016 x2[1] (numeric) 1.0073959403965282 absolute error 2.670384132663628e-05 relative error 0.002650849396389421% Desired digits 16 Estimated correct digits 11 Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 1.899999999999956 x1[1] (closed_form) 2.000269223514601 x1[1] (numeric) 2.000204100625871 absolute error 6.512288873006256e-05 relative error 0.003255706180172961% Desired digits 16 Estimated correct digits 11 Correct digits 5 h 0.0001 x2[1] (closed_form) 1.008985107484426 x2[1] (numeric) 1.0090390216254927 absolute error 5.3914141066702115e-05 relative error 0.005343403055880515% Desired digits 16 Estimated correct digits 11 Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 1.999999999999945 x1[1] (closed_form) 2.000243603509826 x1[1] (numeric) 2.000141085582417 absolute error 0.00010251792740900711 relative error 0.005125272103313766% Desired digits 16 Estimated correct digits 11 Correct digits 5 h 0.0001 x2[1] (closed_form) 1.0109602305915986 x2[1] (numeric) 1.01105582659539 absolute error 9.559600379138722e-05 relative error 0.009455960867565076% Desired digits 16 Estimated correct digits 11 Correct digits 5 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 2.100000000000156 x1[1] (closed_form) 2.0002204215708552 x1[1] (numeric) 2.0000714431889914 absolute error 0.00014897838186378465 relative error 0.007448098232433094% Desired digits 16 Estimated correct digits 11 Correct digits 5 h 0.0001 x2[1] (closed_form) 1.0133740031366651 x2[1] (numeric) 1.0135301442799756 absolute error 0.00015614114331041762 relative error 0.015408047061313867% Desired digits 16 Estimated correct digits 11 Correct digits 4 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 2.200000000000367 x1[1] (closed_form) 2.0001994456850523 x1[1] (numeric) 1.9999944764411113 absolute error 0.00020496924394097782 relative error 0.010247440293174238% Desired digits 16 Estimated correct digits 11 Correct digits 4 h 0.0001 x2[1] (closed_form) 1.0163234146805145 x2[1] (numeric) 1.016564424719792 absolute error 0.00024101003927756715 relative error 0.023713911909953356% Desired digits 16 Estimated correct digits 11 Correct digits 4 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 2.300000000000578 x1[1] (closed_form) 2.000180465918701 x1[1] (numeric) 1.999909415029699 absolute error 0.0002710508890018115 relative error 0.0135513216742328% Desired digits 16 Estimated correct digits 11 Correct digits 4 h 0.0001 x2[1] (closed_form) 1.0199269407815266 x2[1] (numeric) 1.0202839221981106 absolute error 0.0003569814165840235 relative error 0.03500068507951009% Desired digits 16 Estimated correct digits 11 Correct digits 4 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 2.400000000000789 x1[1] (closed_form) 2.000163292315921 x1[1] (numeric) 1.9998154076315573 absolute error 0.00034788468436364184 relative error 0.017392814161729667% Desired digits 16 Estimated correct digits 11 Correct digits 4 h 0.0001 x2[1] (closed_form) 1.024329298889772 x2[1] (numeric) 1.0248417569436528 absolute error 0.0005124580538806711 relative error 0.05002864356570715% Desired digits 16 Estimated correct digits 11 Correct digits 4 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 2.500000000001 x1[1] (closed_form) 2.0001477529975227 x1[1] (numeric) 1.999711513389051 absolute error 0.00043623960847161136 relative error 0.021810369149871084% Desired digits 16 Estimated correct digits 11 Correct digits 4 h 0.0001 x2[1] (closed_form) 1.0297072573201618 x2[1] (numeric) 1.0304250988523975 absolute error 0.0007178415322357523 relative error 0.06971316625503372% Desired digits 16 Estimated correct digits 11 Correct digits 4 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 2.600000000001211 x1[1] (closed_form) 2.0001336924407855 x1[1] (numeric) 1.9995966924936697 absolute error 0.0005369999471158682 relative error 0.026848202654921587% Desired digits 16 Estimated correct digits 11 Correct digits 4 h 0.0001 x2[1] (closed_form) 1.0362767304485825 x2[1] (numeric) 1.0372627217879604 absolute error 0.000985991339377934 relative error 0.09514749394701925% Desired digits 16 Estimated correct digits 11 Correct digits 4 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 2.700000000001422 x1[1] (closed_form) 2.000120969922931 x1[1] (numeric) 1.999469795779309 absolute error 0.0006511741436221463 relative error 0.03255673798806466% Desired digits 16 Estimated correct digits 11 Correct digits 4 h 0.0001 x2[1] (closed_form) 1.0443014448947852 x2[1] (numeric) 1.0456342320666432 absolute error 0.0013327871718580298 relative error 0.12762475608681265% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 2.800000000001633 x1[1] (closed_form) 2.0001094581127252 x1[1] (numeric) 1.9993295532209987 absolute error 0.0007799048917265239 relative error 0.038993110530182236% Desired digits 16 Estimated correct digits 11 Correct digits 4 h 0.0001 x2[1] (closed_form) 1.0541035245041948 x2[1] (numeric) 1.0558813419689066 absolute error 0.0017778174647118394 relative error 0.168656818176189% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 2.900000000001844 x1[1] (closed_form) 2.0000990417961013 x1[1] (numeric) 1.999174561224077 absolute error 0.0009244805720243221 relative error 0.04622173965915872% Desired digits 16 Estimated correct digits 11 Correct digits 4 h 0.0001 x2[1] (closed_form) 1.0660764189481904 x2[1] (numeric) 1.0684216412426237 absolute error 0.0023452222944333467 relative error 0.21998632112575794% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 3.0000000000020552 x1[1] (closed_form) 2.000089616723062 x1[1] (numeric) 1.999003268576545 absolute error 0.001086348146516869 relative error 0.05431497356087159% Desired digits 16 Estimated correct digits 11 Correct digits 4 h 0.0001 x2[1] (closed_form) 1.0807006948193891 x2[1] (numeric) 1.083765419871191 absolute error 0.0030647250518018865 relative error 0.283586849392567% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 3.1000000000022663 x1[1] (closed_form) 2.000081088564308 x1[1] (numeric) 1.9988139609240125 absolute error 0.0012671276402955733 relative error 0.06335381337989346% Desired digits 16 Estimated correct digits 11 Correct digits 4 h 0.0001 x2[1] (closed_form) 1.098563322979816 x2[1] (numeric) 1.1025362178981493 absolute error 0.003972894918333303 relative error 0.3616445984703876% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 3.2000000000024773 x1[1] (closed_form) 2.000073371967161 x1[1] (numeric) 1.9986047436118646 absolute error 0.0014686283552964863 relative error 0.07342872395986279% Desired digits 16 Estimated correct digits 11 Correct digits 4 h 0.0001 x2[1] (closed_form) 1.1203812362362062 x2[1] (numeric) 1.1254959277463368 absolute error 0.0051146915101305535 relative error 0.45651349243519823% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 3.3000000000026883 x1[1] (closed_form) 2.0000663897013222 x1[1] (numeric) 1.9983735227229198 absolute error 0.0016928669784024297 relative error 0.08464053929005988% Desired digits 16 Estimated correct digits 11 Correct digits 4 h 0.0001 x2[1] (closed_form) 1.1470301027994054 x2[1] (numeric) 1.1535754572512211 absolute error 0.006545354451815699 relative error 0.5706349324086015% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 3.4000000000028994 x1[1] (closed_form) 2.0000600718859283 x1[1] (numeric) 1.998117984120811 absolute error 0.001942087765117284 relative error 0.09710147172159785% Desired digits 16 Estimated correct digits 11 Correct digits 4 h 0.0001 x2[1] (closed_form) 1.179579470312113 x2[1] (numeric) 1.1879121848804088 absolute error 0.008332714568295874 relative error 0.7064140041442959% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 3.5000000000031104 x1[1] (closed_form) 2.00005435529016 x1[1] (numeric) 1.997835570289306 absolute error 0.002218785000853929 relative error 0.11093623505707356% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 x2[1] (closed_form) 1.2193356909020827 x2[1] (numeric) 1.229895711295798 absolute error 0.010560020393715286 relative error 0.8660470182663829% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 3.6000000000033214 x1[1] (closed_form) 2.0000491827004048 x1[1] (numeric) 1.997523454735874 absolute error 0.002525727964530766 relative error 0.12628329274986158% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 x2[1] (closed_form) 1.2678943499973971 x2[1] (numeric) 1.281223744475792 absolute error 0.013329394478394763 relative error 1.0513016702394902% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 3.7000000000035325 x1[1] (closed_form) 2.0000445023476465 x1[1] (numeric) 1.9971785137031375 absolute error 0.0028659886445090432 relative error 0.14329624371582503% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 x2[1] (closed_form) 1.327204303059438 x2[1] (numeric) 1.3439703624204158 absolute error 0.016766059360977748 relative error 1.2632613774932049% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 3.8000000000037435 x1[1] (closed_form) 2.000040267389341 x1[1] (numeric) 1.9967972949053066 absolute error 0.003242972484034601 relative error 0.16214535961656726% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 x2[1] (closed_form) 1.3996458902553726 x2[1] (numeric) 1.420669394339641 absolute error 0.02102350408426834 relative error 1.502058787200275% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 3.9000000000039545 x1[1] (closed_form) 2.0000364354406024 x1[1] (numeric) 1.9963759829765213 absolute error 0.0036604524640810876 relative error 0.18301928900983747% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 x2[1] (closed_form) 1.488126468102194 x2[1] (numeric) 1.5144162681175122 absolute error 0.02628980001531822 relative error 1.7666374853775415% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 4.000000000004166 x1[1] (closed_form) 2.0000329681499998 x1[1] (numeric) 1.995910361285389 absolute error 0.004122606864610745 relative error 0.20612694541850948% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 x2[1] (closed_form) 1.5961970921049793 x2[1] (numeric) 1.6289924131097937 absolute error 0.032795321004814415 relative error 2.054590950392329% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 4.1000000000039325 x1[1] (closed_form) 2.000029830815723 x1[1] (numeric) 1.995395769733524 absolute error 0.0046340610821988815 relative error 0.23169959821593533% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 x2[1] (closed_form) 1.7281950332748186 x2[1] (numeric) 1.7690172127216452 absolute error 0.040822179446826645 relative error 2.362128038840109% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 4.200000000003699 x1[1] (closed_form) 2.000026992038277 x1[1] (numeric) 1.994827058115714 absolute error 0.005199933922563016 relative error 0.2599931872551197% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 x2[1] (closed_form) 1.889417848219598 x2[1] (numeric) 1.9401336070628346 absolute error 0.050715758843236536 relative error 2.6842002625849064% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 4.300000000003466 x1[1] (closed_form) 2.000024423406222 x1[1] (numeric) 1.9941985345749385 absolute error 0.005825888831283432 relative error 0.2912908844063723% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 x2[1] (closed_form) 2.0863359888478312 x2[1] (numeric) 2.14923479667431 absolute error 0.06289880782647872 relative error 3.014797624289378% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 4.400000000003233 x1[1] (closed_form) 2.0000220992118254 x1[1] (numeric) 1.9935039086363442 absolute error 0.0065181905754811975 relative error 0.32590592764199483% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 x2[1] (closed_form) 2.3268524844661282 x2[1] (numeric) 2.4047411480718606 absolute error 0.07788866360573232 relative error 3.347382961563335% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] 4.500000000003 x1[1] (closed_form) 2.000019996193769 x1[1] (numeric) 1.9927362282500714 absolute error 0.00728376794369745 relative error 0.3641847560303979% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 x2[1] (closed_form) 2.620620118223763 x2[1] (numeric) 2.716938416872795 absolute error 0.09631829864903185 relative error 3.675401023568257% Desired digits 16 Estimated correct digits 11 Correct digits 3 h 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 Finished! Maximum Time Reached before Solution Completed! diff ( x1 , t , 1 ) = 4.0 * x2 - 2.0 * diff ( x2 , t , 1 ) - 2.0 * x1 ; diff ( x2 , t , 2 ) = 3.0 * diff ( x2 , t , 1 ) - 2.0 * x2 - diff ( x1 , t , 2 ) - diff ( x1 , t , 1 ) + x1 ; Iterations 30176 Total Elapsed Time 3 Minutes 0 Seconds Elapsed Time(since restart) 3 Minutes 0 Seconds Expected Time Remaining 3 Minutes 27.712496271615123 Seconds Optimized Time Remaining 3 Minutes 27.712496271615123 Seconds Expected Total Time 6 Minutes 27.712496271615123 Seconds Time to Timeout 0.0 Seconds Percent Done 46.42615384619937%