Initializing... Initialized Initializing(2)... PI = 0.314159265358979323846264338327950271e1+/-0.313e-33 E = 0.271828182845904523536028747135266232e1+/-0.256e-32 LOG_E_10 = 0.230258509299404568401799145468436324e1+/-0.5e-32 Initialized(2) ##############ECHO OF PROBLEM################# ##############temp/mult_sin_linpostode.ode################# diff ( y , x , 1 ) = sin ( x ) * ( 0.2 * x + 0.3 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(0.1) x_end=c(5.0) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true # 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=(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=true $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(c(0.2) * sin(c(x)) - c(0.2) * cos(c(x)) * c(x) - c(0.3) * cos(c(x))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.1e0+/-0.50e-33 y[1] (closed_form) -0.29843464955960261468921699641511408e0+/-0.843e-33 y[1] (numeric) -0.29843464955960261468921699641511408e0+/-0.114e-32 $glob_prec 0.1e-15+/-0.50e-49% absolute error 0.0e0+/-0.1983e-32 relative error 0.0e0+/-0.664467079451496548458871612304493086e-30% Desired digits 8 Estimated correct digits 14 Correct digits 34 h 0.1e-2+/-0.5e-33 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] 0.11e0+/-0.550e-32 y[1] (closed_form) -0.29809820337462142408223445686050013e0+/-0.301e-32 y[1] (numeric) -0.29809820337462142408223451758412392e0+/-0.684e-32 absolute error 0.6072362379e-25+/-0.985e-32 relative error 0.203703420894785918498047788832879421e-22+/-0.33e-29% Desired digits 8 Estimated correct digits 13 Correct digits 23 h 0.1e-2+/-0.5e-33 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] 0.12e0+/-0.105e-31 y[1] (closed_form) -0.29772755655886879373491368353167942e0+/-0.518e-32 y[1] (numeric) -0.2977275565588687937349138043363648e0+/-0.116e-31 absolute error 0.12080468538e-24+/-0.167e-31 relative error 0.405755808351295977574129555201689325e-22+/-0.56e-29% Desired digits 8 Estimated correct digits 13 Correct digits 23 h 0.1e-2+/-0.5e-33 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] 0.13e0+/-0.155e-31 y[1] (closed_form) -0.29732234882708192899956980565382926e0+/-0.742e-32 y[1] (numeric) -0.29732234882708192899956998588438307e0+/-0.152e-31 absolute error 0.18023055381e-24+/-0.226e-31 relative error 0.606178965425903107547706188591119823e-22+/-0.76e-29% Desired digits 8 Estimated correct digits 13 Correct digits 23 h 0.1e-2+/-0.5e-33 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] 0.14e0+/-0.205e-31 y[1] (closed_form) -0.29688222382889769603925734811866496e0+/-0.966e-32 y[1] (numeric) -0.29688222382889769603925758710733659e0+/-0.188e-31 absolute error 0.23898867163e-24+/-0.284e-31 relative error 0.804994885001051728514042082686985472e-22+/-0.956e-29% Desired digits 8 Estimated correct digits 13 Correct digits 23 h 0.1e-2+/-0.5e-33 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] 0.15e0+/-0.255e-31 y[1] (closed_form) -0.29640682922417411032299864181840349e0+/-0.119e-31 y[1] (numeric) -0.29640682922417411032299893888496025e0+/-0.222e-31 absolute error 0.29706655676e-24+/-0.341e-31 relative error 0.100222575012037571551350736600213181e-21+/-0.115e-28% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 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] 0.16e0+/-0.305e-31 y[1] (closed_form) -0.29589581675785895441930360603689018e0+/-0.142e-31 y[1] (numeric) -0.29589581675785895441930396048869462e0+/-0.256e-31 absolute error 0.35445180444e-24+/-0.398e-31 relative error 0.119789393552007965709636035631873299e-21+/-0.134e-28% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 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] 0.17e0+/-0.355e-31 y[1] (closed_form) -0.29534884233439407483189974139680573e0+/-0.166e-31 y[1] (numeric) -0.29534884233439407483190015252889477e0+/-0.292e-31 absolute error 0.41113208904e-24+/-0.458e-31 relative error 0.139202200960217777983852025098107082e-21+/-0.155e-28% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 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] 0.18e0+/-0.405e-31 y[1] (closed_form) -0.29476556609164395963479203632963363e0+/-0.189e-31 y[1] (numeric) -0.29476556609164395963479250342479968e0+/-0.326e-31 absolute error 0.46709516605e-24+/-0.515e-31 relative error 0.158463273795277017305028886503288084e-21+/-0.174e-28% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 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] 0.19e0+/-0.455e-31 y[1] (closed_form) -0.29414565247433725221257236581992954e0+/-0.214e-31 y[1] (numeric) -0.29414565247433725221257288814880346e0+/-0.362e-31 absolute error 0.52232887392e-24+/-0.576e-31 relative error 0.177574908731846920960903437618575099e-21+/-0.195e-28% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 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+/-0.505e-31 y[1] (closed_form) -0.29348877030700991149034429027069946e0+/-0.236e-31 y[1] (numeric) -0.29348877030700991149034486709183542e0+/-0.396e-31 absolute error 0.57682113596e-24+/-0.632e-31 relative error 0.196539423077961208248178625284022265e-21+/-0.215e-28% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 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] 0.21e0+/-0.555e-31 y[1] (closed_form) -0.29279459286643878563957690504444784e0+/-0.262e-31 y[1] (numeric) -0.29279459286643878563957753560440998e0+/-0.43e-31 absolute error 0.63055996214e-24+/-0.692e-31 relative error 0.21535915536105419239643342579930075e-21+/-0.236e-28% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 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] 0.22e0+/-0.605e-31 y[1] (closed_form) -0.29206279795355442436531370438797292e0+/-0.289e-31 y[1] (numeric) -0.29206279795355442436531438792142395e0+/-0.466e-31 absolute error 0.68353345103e-24+/-0.755e-31 relative error 0.234036466068061014693281205398095283e-21+/-0.258e-28% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 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] 0.23e0+/-0.655e-31 y[1] (closed_form) -0.29129306796482201450991136176075887e0+/-0.313e-31 y[1] (numeric) -0.29129306796482201450991209749055042e0+/-0.5e-31 absolute error 0.73572979155e-24+/-0.813e-31 relative error 0.252573738431307384581201136677857518e-21+/-0.279e-28% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 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] 0.24e0+/-0.705e-31 y[1] (closed_form) -0.29048508996307938484215056904529284e0+/-0.338e-31 y[1] (numeric) -0.29048508996307938484215135618255775e0+/-0.532e-31 absolute error 0.78713726491e-24+/-0.870e-31 relative error 0.270973379394462221309344540011664412e-21+/-0.299e-28% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 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] 0.25e0+/-0.755e-31 y[1] (closed_form) -0.28963855574782108853123866635308837e0+/-0.364e-31 y[1] (numeric) -0.28963855574782108853123950409733468e0+/-0.57e-31 absolute error 0.83774424631e-24+/-0.934e-31 relative error 0.289237820616464055146914765832808505e-21+/-0.322e-28% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 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] 0.26e0+/-0.805e-31 y[1] (closed_form) -0.28875316192491763592581491867737855e0+/-0.391e-31 y[1] (numeric) -0.28875316192491763592581580621658537e0+/-0.602e-31 absolute error 0.88753920682e-24+/-0.993e-31 relative error 0.307369519662880887103968104309344153e-21+/-0.343e-28% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 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] 0.27e0+/-0.855e-31 y[1] (closed_form) -0.28782860997575901586128907495613185e0+/-0.418e-31 y[1] (numeric) -0.28782860997575901586129001146684706e0+/-0.64e-31 absolute error 0.93651071521e-24+/-0.105e-30 relative error 0.325370961312314687245194097843572814e-21+/-0.364e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 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] 0.28e0+/-0.905e-31 y[1] (closed_form) -0.2868646063258117107972201473887762e0+/-0.445e-31 y[1] (numeric) -0.28686460632581171079722113203621587e0+/-0.672e-31 absolute error 0.98464743967e-24+/-0.111e-30 relative error 0.343244658963493287983725209582717557e-21+/-0.386e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 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] 0.29e0+/-0.955e-31 y[1] (closed_form) -0.28586086241257847963231662939873231e0+/-0.472e-31 y[1] (numeric) -0.28586086241257847963231766133688198e0+/-0.706e-31 absolute error 0.103193814967e-23+/-0.117e-30 relative error 0.360993156237183642306344944225566039e-21+/-0.409e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 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+/-0.1e-30 y[1] (closed_form) -0.28481709475295025205016753278749248e0+/-0.497e-31 y[1] (numeric) -0.28481709475295025205016861115921007e0+/-0.74e-31 absolute error 0.107837171759e-23+/-0.123e-30 relative error 0.37861902865253834429292242793224526e-21+/-0.431e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 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] 0.31e0+/-0.1e-30 y[1] (closed_form) -0.2837330250099395497059669031134072e0+/-0.5e-31 y[1] (numeric) -0.28373302500993954970596802705052779e0+/-0.772e-31 absolute error 0.112393712059e-23+/-0.127e-30 relative error 0.39612488555064288695437880149931531e-21+/-0.447e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 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] 0.32e0+/-0.1e-30 y[1] (closed_form) -0.28260838005878492246506033896742782e0+/-0.504e-31 y[1] (numeric) -0.28260838005878492246506150759087016e0+/-0.81e-31 absolute error 0.116862344234e-23+/-0.131e-30 relative error 0.413513372143075334426755762193522033e-21+/-0.463e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 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] 0.33e0+/-0.1e-30 y[1] (closed_form) -0.28144289205241596223972513244798717e0+/-0.506e-31 y[1] (numeric) -0.28144289205241596223972634486786189e0+/-0.847e-31 absolute error 0.121241987472e-23+/-0.135e-30 relative error 0.430787171734363345985705778498418589e-21+/-0.479e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 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] 0.34e0+/-0.1e-30 y[1] (closed_form) -0.28023629848626853273261871668362278e0+/-0.511e-31 y[1] (numeric) -0.28023629848626853273261997199934227e0+/-0.897e-31 absolute error 0.125531571949e-23+/-0.14e-30 relative error 0.44794900813019051899372565923833686e-21+/-0.499e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 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] 0.35e0+/-0.1e-30 y[1] (closed_form) -0.27898834226243993057503499081883029e0+/-0.514e-31 y[1] (numeric) -0.27898834226243993057503628811922038e0+/-0.947e-31 absolute error 0.129730039009e-23+/-0.146e-30 relative error 0.465001648301723660203761507621914996e-21+/-0.523e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 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! Maximum Time Reached before Solution Completed! diff ( y , x , 1 ) = sin ( x ) * ( 0.2 * x + 0.3 ) ; Iterations 260 Total Elapsed Time 3 Minutes 0 Seconds Elapsed Time(since restart) 2 Minutes 59 Seconds Expected Time Remaining 53 Minutes 19 Seconds Optimized Time Remaining 53 Minutes 1 Seconds Expected Total Time 56 Minutes 1 Seconds Time to Timeout 0 Seconds Percent Done 0.53265306122448979591836734693877551e1+/-0.204e-29%