Initializing... Initialized Initializing(2)... PI = 0.3141592653589793238462643383279486e1+/-0.313e-31 E = 0.2718281828459045235360287471352649e1+/-0.256e-30 LOG_E_10 = 0.2302585092994045684017991454684277e1+/-0.5e-30 Initialized(2) ##############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=(20.0) $glob_subiter_method=3 $glob_max_iter=1000 $glob_upper_ratio_limit=c(1.11) $glob_lower_ratio_limit=c(0.99) # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb #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] -0.14e1+/-0.50e-30 y[1] (closed_form) 0.1095055278569960754634732377446509e1+/-0.159e-28 y[1] (numeric) 0.1095055278569960754634732377446509e1+/-0.159e-28 absolute error 0.0e0+/-0.318e-28 relative error 0.0e0+/-0.2903962989113007191308033034320142e-26% Desired digits 8 Estimated correct digits 11 Correct digits 32 h 0.5e-1+/-0.1e-100 SETTING H FOR POLE Radius of convergence (given) for eq 1 0.1000000000000000000000000000001722e0+/-0.219e-29 Order of pole (given) 0.5e0+/-0.50e-31 Radius of convergence (ratio test) for eq 1 0.111439570202913182550517298740244e0+/-0.642e-27 Order of pole (ratio test) 0.9999999999994611784271558639651198e0+/-0.5e-31 Radius of convergence (three term test) for eq 1 0.996710879465263979103032962393583e-1+/-0.266e-25 Order of pole (three term test) 0.1639818332457102882709215011242036e1+/-0.763e-23 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.13003289120534736020896967037606e1+/-0.262e-25 y[1] (closed_form) 0.118017468138312141013958512534519e1+/-0.727e-24 y[1] (numeric) 0.1180652748830341382814539445279324e1+/-0.347e-25 absolute error 0.478067447219972674954319934134e-3+/-0.761e-24 relative error 0.4050819380904657042130058989766109e-1+/-0.644e-22% Desired digits 8 Estimated correct digits 11 Correct digits 4 h 0.996710879465263979103032962393583e-2+/-0.266e-26 Radius of convergence (given) for eq 1 0.1996710879465263979103032962394192e0+/-0.519e-25 Order of pole (given) 0.5e0+/-0.50e-31 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 Finished! diff ( y , x , 1 ) = cos ( sqrt ( 2.0 * x + 3.0 ) ) ; Iterations 11 Total Elapsed Time 32 Seconds Elapsed Time(since restart) 30 Seconds Time to Timeout 19 Minutes 28 Seconds Percent Done 0.11960530553583167749236395548728e3+/-0.314e-22%