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/sinpostode.ode################# diff ( y , x , 1 ) = sin ( x ) ; ! #BEGIN FIRST INPUT BLOCK # ELIMINATED in preodein.rb # Digits:=16; ELIMINATED in preodein.rb max_terms=40 # ELIMINATED in preodein.rb ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK # ELIMINATED in preodein.rb x_start=c(0.0) x_end=c(1.0) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=false # 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=3 # 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(c(2.0) - cos(c(x))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.0e0+/-0.50e-31 y[1] (closed_form) 0.1e1+/-0.55e-31 y[1] (numeric) 0.1e1+/-0.155e-30 absolute error 0.0e0+/-0.210e-30 relative error 0.0e0+/-0.2100000000000000000000000000000231e-28% Desired digits 8 Estimated correct digits 14 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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 TOP MAIN SOLVE Loop x[1] 0.1e0+/-0.2e-100 y[1] (closed_form) 0.100499583472197423390443801219613e1+/-0.558e-31 y[1] (numeric) 0.1004995834721974233904542133730804e1+/-0.555e-30 absolute error 0.104121534674e-21+/-0.61e-30 relative error 0.1036039464808374719193323239214324e-19+/-0.606e-28% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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 TOP MAIN SOLVE Loop x[1] 0.2e0+/-0.4e-100 y[1] (closed_form) 0.1019933422158758368875803483251831e1+/-0.583e-31 y[1] (numeric) 0.1019933422158758368876426918793744e1+/-0.957e-30 absolute error 0.623435541913e-21+/-0.101e-29 relative error 0.6112512134306338618859348890098377e-19+/-0.99e-28% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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 TOP MAIN SOLVE Loop x[1] 0.3e0+/-0.6e-100 y[1] (closed_form) 0.104466351087439398035768977243195e1+/-0.626e-31 y[1] (numeric) 0.1044663510874393980359242525639767e1+/-0.11e-29 absolute error 0.1552753207817e-20+/-0.116e-29 relative error 0.1486366846026171410190703968951343e-18+/-0.111e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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 TOP MAIN SOLVE Loop x[1] 0.4e0+/-0.8e-100 y[1] (closed_form) 0.1078939005997114917201473267948199e1+/-0.687e-31 y[1] (numeric) 0.1078939005997114917204356057045659e1+/-0.12e-29 absolute error 0.288278909746e-20+/-0.126e-29 relative error 0.2671874018305450510119052600143182e-18+/-0.116e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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 TOP MAIN SOLVE Loop x[1] 0.5e0+/-0.10e-99 y[1] (closed_form) 0.112241743810962728388371841739617e1+/-0.769e-31 y[1] (numeric) 0.1122417438109627283888318671328057e1+/-0.13e-29 absolute error 0.4600253931887e-20+/-0.137e-29 relative error 0.4098523219342294316287298072128181e-18+/-0.122e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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 TOP MAIN SOLVE Loop x[1] 0.6e0+/-0.12e-99 y[1] (closed_form) 0.1174664385090321702759047501044624e1+/-0.823e-31 y[1] (numeric) 0.1174664385090321702765735488414811e1+/-0.145e-29 absolute error 0.6687987370187e-20+/-0.153e-29 relative error 0.5693530386275183307614496196264993e-18+/-0.13e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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 TOP MAIN SOLVE Loop x[1] 0.7e0+/-0.14e-99 y[1] (closed_form) 0.1235157812715511573744140009808135e1+/-0.997e-31 y[1] (numeric) 0.1235157812715511573753265139278095e1+/-0.157e-29 absolute error 0.912512946996e-20+/-0.166e-29 relative error 0.73878247589255630115346334636133e-18+/-0.134e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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 TOP MAIN SOLVE Loop x[1] 0.8e0+/-0.16e-99 y[1] (closed_form) 0.1303293290652834579079250018357675e1+/-0.115e-30 y[1] (numeric) 0.1303293290652834579091137347470631e1+/-0.169e-29 absolute error 0.11887329112956e-19+/-0.18e-29 relative error 0.9120993101254668707730141932741677e-18+/-0.138e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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 TOP MAIN SOLVE Loop x[1] 0.9e0+/-0.18e-99 y[1] (closed_form) 0.1378390031729335543515283848592866e1+/-0.132e-30 y[1] (numeric) 0.137839003172933554353023083590627e1+/-0.187e-29 absolute error 0.14946987313404e-19+/-0.2e-29 relative error 0.1084380107903960199654623764901711e-17+/-0.145e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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 Finished! diff ( y , x , 1 ) = sin ( x ) ; Iterations 20 Total Elapsed Time 27 Seconds Elapsed Time(since restart) 27 Seconds Time to Timeout 19 Minutes 33 Seconds Percent Done 0.105e3+/-0.105e-28%