##############ECHO OF PROBLEM################# ##############temp/cos_sqrt_linpostode.ode################# diff ( y , x , 1 ) = cos ( sqrt ( 2.0 * x + 3.0 ) ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(-1.4) x_end=c(-1.3) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_h=0.0001 $glob_upper_ratio_limit=c(1.001) $glob_lower_ratio_limit=c(0.999) # 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 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=1 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=c(-1.5) # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=c(0.0) # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=c(0.5) # ELIMINATED in preodein.rb $array_given_ord_poles[1][2]=c(0.0) # ELIMINATED in preodein.rb #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=8 $glob_max_minutes=(3.0) $glob_subiter_method=3 $glob_max_iter=100000 $glob_upper_ratio_limit=c(1.000001) $glob_lower_ratio_limit=c(0.999999) $glob_look_poles=false $glob_h=c(0.001) $glob_display_interval=c(0.01) #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) x = c(x) return(cos(sqrt(c(2.0)*c(x)+c(3.0)))+sqrt(c(2.0)*c(x)+c(3.0))*sin(sqrt(c(2.0)*c(x)+c(3.0)))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] -1.4 y[1] (closed_form) 1.0950552785699608 y[1] (numeric) 1.0950552785699608 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 14 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] -1.390000000000001 y[1] (closed_form) 1.1040235390255817 y[1] (numeric) 1.1040283738053158 absolute error 4.834779734119721e-06 relative error 0.0004379236097073554% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] -1.3800000000000021 y[1] (closed_form) 1.1128954259704735 y[1] (numeric) 1.1129050785335752 absolute error 9.652563101703038e-06 relative error 0.0008673378357437091% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] -1.3700000000000032 y[1] (closed_form) 1.1216712651341294 y[1] (numeric) 1.1216857186282405 absolute error 1.4453494111110743e-05 relative error 0.001288567743543149% Desired digits 8 Estimated correct digits 13 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] -1.3600000000000043 y[1] (closed_form) 1.1303513815907278 y[1] (numeric) 1.1303706192826644 absolute error 1.923769193656888e-05 relative error 0.0017019213892140285% Desired digits 8 Estimated correct digits 13 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] -1.3500000000000054 y[1] (closed_form) 1.1389360997600726 y[1] (numeric) 1.1389601050178462 absolute error 2.4005257773573874e-05 relative error 0.0021076913602642677% Desired digits 8 Estimated correct digits 13 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] -1.3400000000000065 y[1] (closed_form) 1.1474257434085307 y[1] (numeric) 1.1474544996880134 absolute error 2.8756279482733405e-05 relative error 0.002506156032137671% Desired digits 8 Estimated correct digits 13 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] -1.3300000000000076 y[1] (closed_form) 1.1558206356499694 y[1] (numeric) 1.155854126484788 absolute error 3.3490834818517e-05 relative error 0.002897580626745223% Desired digits 8 Estimated correct digits 13 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] -1.3200000000000087 y[1] (closed_form) 1.1641210989466924 y[1] (numeric) 1.1641593079404258 absolute error 3.820899373341291e-05 relative error 0.003282218127305206% Desired digits 8 Estimated correct digits 13 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] -1.3100000000000098 y[1] (closed_form) 1.1723274551103748 y[1] (numeric) 1.1723703659304325 absolute error 4.291082005769553e-05 relative error 0.0036603100840673793% Desired digits 8 Estimated correct digits 13 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] -1.300000000000011 y[1] (closed_form) 1.180440025302998 y[1] (numeric) 1.1804876216757467 absolute error 4.7596372748648363e-05 relative error 0.004032087334249041% Desired digits 8 Estimated correct digits 13 Correct digits 5 h 0.001 Finished! diff ( y , x , 1 ) = cos ( sqrt ( 2.0 * x + 3.0 ) ) ; Iterations 101 Total Elapsed Time 1 Seconds Elapsed Time(since restart) 1 Seconds Time to Timeout 2 Minutes 59.0 Seconds Percent Done 101.9999999999889%