##############ECHO OF PROBLEM################# ##############temp/lin_arcsin_m0d5_0d5postode.ode################# diff ( y , x , 1 ) = arcsin ( x + 0.0001 ) ; ! // BEGIN FIRST INPUT BLOCK max_terms=30; Digits=32; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(-0.5); x_end=c(0.5); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_display_interval=0.0001; glob_type_given_pole=0; // 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 double exact_soln_y (double x) { return((c(x) + c(0.0001)) * arcsin(c(x) + c(0.0001)) + sqrt(c(1.0) - (c(x) + c(0.0001)) * (c(x) +c(0.0001)))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = -0.5 y[1] (closed_form) = 1.127772437479403 y[1] (numeric) = 1.127772437479403 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.49 y[1] (closed_form) = 1.122595208585987 y[1] (numeric) = 1.122595209844472 absolute error = 1.258484649824254e-09 relative error = 1.121049368640574e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.48 y[1] (closed_form) = 1.117532690160805 y[1] (numeric) = 1.117532692628719 absolute error = 2.467913429171631e-09 relative error = 2.208359049269973e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.47 y[1] (closed_form) = 1.112584157157668 y[1] (numeric) = 1.11258416078811 absolute error = 3.630442169111348e-09 relative error = 3.26307196247166e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.46 y[1] (closed_form) = 1.107748912646826 y[1] (numeric) = 1.107748917394906 absolute error = 4.748079485139556e-09 relative error = 4.286241612094766e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.45 y[1] (closed_form) = 1.103026286610786 y[1] (numeric) = 1.103026292433487 absolute error = 5.822700988034057e-09 relative error = 5.278841545948266e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4399999999999999 y[1] (closed_form) = 1.09841563482041 y[1] (numeric) = 1.098415641676469 absolute error = 6.856058831772316e-09 relative error = 6.241770978517868e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4299999999999999 y[1] (closed_form) = 1.093916337784892 y[1] (numeric) = 1.093916345634685 absolute error = 7.849792149627888e-09 relative error = 7.17586151562851e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4199999999999999 y[1] (closed_form) = 1.089527799769821 y[1] (numeric) = 1.089527808575255 absolute error = 8.805433937553175e-09 relative error = 8.081880920719465e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4099999999999999 y[1] (closed_form) = 1.085249447878089 y[1] (numeric) = 1.08524945760251 absolute error = 9.724421712320463e-09 relative error = 8.960540575564388e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3999999999999999 y[1] (closed_form) = 1.081080731188917 y[1] (numeric) = 1.081080741797019 absolute error = 1.060810217445862e-08 relative error = 9.812497687191572e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3899999999999999 y[1] (closed_form) = 1.077021119950699 y[1] (numeric) = 1.077021131408437 absolute error = 1.145773831368047e-08 relative error = 1.063835991833191e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3799999999999999 y[1] (closed_form) = 1.07307010482375 y[1] (numeric) = 1.073070117098267 absolute error = 1.227451673635471e-08 relative error = 1.143869042775242e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3699999999999999 y[1] (closed_form) = 1.069227196169424 y[1] (numeric) = 1.069227209228976 absolute error = 1.305955166230888e-08 relative error = 1.221400999628102e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3599999999999999 y[1] (closed_form) = 1.065491923382352 y[1] (numeric) = 1.065491937196242 absolute error = 1.381389003185518e-08 relative error = 1.296480032246858e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3499999999999999 y[1] (closed_form) = 1.061863834262858 y[1] (numeric) = 1.061863848801375 absolute error = 1.453851661281647e-08 relative error = 1.369150746424004e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3399999999999999 y[1] (closed_form) = 1.058342494426856 y[1] (numeric) = 1.058342509661215 absolute error = 1.523435821937369e-08 relative error = 1.439454458230351e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3299999999999998 y[1] (closed_form) = 1.054927486750761 y[1] (numeric) = 1.054927502653047 absolute error = 1.590228571046737e-08 relative error = 1.507429269801979e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3199999999999998 y[1] (closed_form) = 1.051618410849154 y[1] (numeric) = 1.051618427392274 absolute error = 1.654311998500191e-08 relative error = 1.573110532711554e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3099999999999998 y[1] (closed_form) = 1.048414882583147 y[1] (numeric) = 1.048414899740781 absolute error = 1.715763331411324e-08 relative error = 1.636530880965676e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2999999999999998 y[1] (closed_form) = 1.04531653359753 y[1] (numeric) = 1.045316551344083 absolute error = 1.774655289388249e-08 relative error = 1.697720482120998e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2899999999999998 y[1] (closed_form) = 1.042323010884976 y[1] (numeric) = 1.042323029195539 absolute error = 1.831056284373744e-08 relative error = 1.756707148601757e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2799999999999998 y[1] (closed_form) = 1.039433976375691 y[1] (numeric) = 1.039433995226 absolute error = 1.88503086473446e-08 relative error = 1.81351669040799e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2699999999999998 y[1] (closed_form) = 1.036649106551044 y[1] (numeric) = 1.036649125917441 absolute error = 1.936639715260924e-08 relative error = 1.868172849445817e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2599999999999998 y[1] (closed_form) = 1.033968092079809 y[1] (numeric) = 1.033968111939208 absolute error = 1.985939923621061e-08 relative error = 1.920697494277968e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2499999999999998 y[1] (closed_form) = 1.031390637475792 y[1] (numeric) = 1.031390657805644 absolute error = 2.032985291222644e-08 relative error = 1.971110864645949e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2399999999999998 y[1] (closed_form) = 1.028916460775666 y[1] (numeric) = 1.02891648155393 absolute error = 2.077826377622216e-08 relative error = 2.019431564012311e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2299999999999998 y[1] (closed_form) = 1.026545293235984 y[1] (numeric) = 1.026545314441091 absolute error = 2.12051067816077e-08 relative error = 2.06567668483119e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2199999999999998 y[1] (closed_form) = 1.024276879048359 y[1] (numeric) = 1.024276900659188 absolute error = 2.161082912621737e-08 relative error = 2.109862046900413e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2099999999999997 y[1] (closed_form) = 1.022110975071937 y[1] (numeric) = 1.022110997067786 absolute error = 2.199584892004225e-08 relative error = 2.152002028790871e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1999999999999997 y[1] (closed_form) = 1.020047350582326 y[1] (numeric) = 1.020047372942886 absolute error = 2.236055984816687e-08 relative error = 2.19210998738457e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1899999999999997 y[1] (closed_form) = 1.018085787036199 y[1] (numeric) = 1.018085809741528 absolute error = 2.270532939441239e-08 relative error = 2.230198052416686e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1799999999999997 y[1] (closed_form) = 1.01622607785088 y[1] (numeric) = 1.016226100881382 absolute error = 2.303050194996104e-08 relative error = 2.266277401448509e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1699999999999997 y[1] (closed_form) = 1.014468028198271 y[1] (numeric) = 1.014468051534669 absolute error = 2.333639836926693e-08 relative error = 2.300358189770964e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1599999999999997 y[1] (closed_form) = 1.012811454812484 y[1] (numeric) = 1.012811478435801 absolute error = 2.362331774641291e-08 relative error = 2.332449700698403e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1499999999999997 y[1] (closed_form) = 1.011256185810676 y[1] (numeric) = 1.011256209702214 absolute error = 2.389153741511052e-08 relative error = 2.362560323520574e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1399999999999997 y[1] (closed_form) = 1.009802060526542 y[1] (numeric) = 1.009802084667857 absolute error = 2.414131516914608e-08 relative error = 2.390697752840596e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1299999999999997 y[1] (closed_form) = 1.008448929356019 y[1] (numeric) = 1.008448953728909 absolute error = 2.43728899285145e-08 relative error = 2.41686903709429e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1199999999999997 y[1] (closed_form) = 1.007196653614777 y[1] (numeric) = 1.007196678201257 absolute error = 2.45864799630624e-08 relative error = 2.441080386320069e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1099999999999997 y[1] (closed_form) = 1.006045105407103 y[1] (numeric) = 1.006045130189388 absolute error = 2.478228555702344e-08 relative error = 2.4633374213371e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.09999999999999964 y[1] (closed_form) = 1.004994167505832 y[1] (numeric) = 1.004994192466321 absolute error = 2.496048945310747e-08 relative error = 2.483645205131265e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.08999999999999964 y[1] (closed_form) = 1.004043733242998 y[1] (numeric) = 1.004043758364255 absolute error = 2.512125707454516e-08 relative error = 2.502008253505561e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.07999999999999963 y[1] (closed_form) = 1.003193706410922 y[1] (numeric) = 1.003193731675659 absolute error = 2.526473652508798e-08 relative error = 2.518430524796295e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.06999999999999962 y[1] (closed_form) = 1.002444001173479 y[1] (numeric) = 1.00244402656454 absolute error = 2.539106014332049e-08 relative error = 2.532915565717112e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.05999999999999961 y[1] (closed_form) = 1.001794541987309 y[1] (numeric) = 1.001794567487652 absolute error = 2.550034294834802e-08 relative error = 2.545466348594966e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.0499999999999996 y[1] (closed_form) = 1.00124526353277 y[1] (numeric) = 1.001245289125454 absolute error = 2.559268419410898e-08 relative error = 2.55608541945141e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.03999999999999959 y[1] (closed_form) = 1.000796110654466 y[1] (numeric) = 1.000796136322634 absolute error = 2.566816759141943e-08 relative error = 2.564774914506198e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.02999999999999958 y[1] (closed_form) = 1.00044703831118 y[1] (numeric) = 1.000447064038042 absolute error = 2.57268619741069e-08 relative error = 2.571536622022043e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.01999999999999957 y[1] (closed_form) = 1.000198011535106 y[1] (numeric) = 1.000198037303926 absolute error = 2.576881996674274e-08 relative error = 2.576371845330175e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.009999999999999565 y[1] (closed_form) = 1.00004900540026 y[1] (numeric) = 1.00004903119434 absolute error = 2.579407953895441e-08 relative error = 2.579281555170446e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.371503159461554e-16 y[1] (closed_form) = 1.000000005 y[1] (numeric) = 1.000000030802664 absolute error = 2.580266400542541e-08 relative error = 2.580266387641209e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.01000000000000044 y[1] (closed_form) = 1.000051005433598 y[1] (numeric) = 1.000051031228179 absolute error = 2.579458024953851e-08 relative error = 2.579326465289098e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.02000000000000045 y[1] (closed_form) = 1.000202011801828 y[1] (numeric) = 1.000202037571649 absolute error = 2.576982094382174e-08 relative error = 2.576461618728235e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.03000000000000046 y[1] (closed_form) = 1.000453039211555 y[1] (numeric) = 1.000453064939919 absolute error = 2.572836454994842e-08 relative error = 2.57167138701729e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.04000000000000047 y[1] (closed_form) = 1.00080411278935 y[1] (numeric) = 1.000804138459523 absolute error = 2.56701722101127e-08 relative error = 2.564954708126361e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.05000000000000047 y[1] (closed_form) = 1.001255267704148 y[1] (numeric) = 1.001255293299341 absolute error = 2.559519307610003e-08 relative error = 2.556310453655753e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.06000000000000048 y[1] (closed_form) = 1.001806549199018 y[1] (numeric) = 1.001806574702377 absolute error = 2.550335898021672e-08 relative error = 2.545736899065754e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.07000000000000049 y[1] (closed_form) = 1.002458012632121 y[1] (numeric) = 1.002458038026707 absolute error = 2.539458598960209e-08 relative error = 2.533231882991725e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.0800000000000005 y[1] (closed_form) = 1.003209723526956 y[1] (numeric) = 1.003209748795731 absolute error = 2.526877573849617e-08 relative error = 2.518792944874923e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.09000000000000051 y[1] (closed_form) = 1.004061757632031 y[1] (numeric) = 1.004061782757844 absolute error = 2.512581298574901e-08 relative error = 2.502417086873766e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1000000000000005 y[1] (closed_form) = 1.005014200990098 y[1] (numeric) = 1.005014225955664 absolute error = 2.496556561482066e-08 relative error = 2.484100780887039e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1100000000000005 y[1] (closed_form) = 1.006067150017138 y[1] (numeric) = 1.006067174805025 absolute error = 2.478788707627189e-08 relative error = 2.463840219397844e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1200000000000005 y[1] (closed_form) = 1.007220711591297 y[1] (numeric) = 1.007220736183909 absolute error = 2.459261261300583e-08 relative error = 2.441630948409732e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1300000000000005 y[1] (closed_form) = 1.008475003152004 y[1] (numeric) = 1.008475027531563 absolute error = 2.437955926026802e-08 relative error = 2.4174678781397e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1400000000000005 y[1] (closed_form) = 1.009830152809532 y[1] (numeric) = 1.00983017695806 absolute error = 2.414852739995865e-08 relative error = 2.391345448813648e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1500000000000005 y[1] (closed_form) = 1.011286299465283 y[1] (numeric) = 1.011286323364582 absolute error = 2.389929854018646e-08 relative error = 2.36325742302879e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1600000000000006 y[1] (closed_form) = 1.01284359294313 y[1] (numeric) = 1.012843616574765 absolute error = 2.36316355373134e-08 relative error = 2.333196922206358e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000006 y[1] (closed_form) = 1.014502194132156 y[1] (numeric) = 1.014502217477437 absolute error = 2.334528148573156e-08 relative error = 2.301156332707788e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1800000000000006 y[1] (closed_form) = 1.016262275141193 y[1] (numeric) = 1.016262298181152 absolute error = 2.303995882968479e-08 relative error = 2.26712723607533e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1900000000000006 y[1] (closed_form) = 1.018124019465572 y[1] (numeric) = 1.018124042180941 absolute error = 2.271536891917947e-08 relative error = 2.231100385108594e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2000000000000006 y[1] (closed_form) = 1.020087622166556 y[1] (numeric) = 1.020087644537748 absolute error = 2.23711922320291e-08 relative error = 2.193065747088972e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2100000000000006 y[1] (closed_form) = 1.022153290063964 y[1] (numeric) = 1.022153312071049 absolute error = 2.200708482114067e-08 relative error = 2.153012178805736e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000006 y[1] (closed_form) = 1.024321241942537 y[1] (numeric) = 1.024321263565217 absolute error = 2.162267942473761e-08 relative error = 2.110927562502956e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000006 y[1] (closed_form) = 1.02659170877264 y[1] (numeric) = 1.026591729990225 absolute error = 2.121758435613685e-08 relative error = 2.066798725805404e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000006 y[1] (closed_form) = 1.028964933945962 y[1] (numeric) = 1.028964954737343 absolute error = 2.079138106125811e-08 relative error = 2.020611235168681e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000006 y[1] (closed_form) = 1.031441173526912 y[1] (numeric) = 1.031441193870536 absolute error = 2.034362389657929e-08 relative error = 1.972349409614536e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000006 y[1] (closed_form) = 1.034020696520487 y[1] (numeric) = 1.034020716394326 absolute error = 1.987383879686888e-08 relative error = 1.921996229257788e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000006 y[1] (closed_form) = 1.036703785157439 y[1] (numeric) = 1.036703804538959 absolute error = 1.938152038860608e-08 relative error = 1.869533097697981e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000006 y[1] (closed_form) = 1.039490735197639 y[1] (numeric) = 1.039490754063771 absolute error = 1.886613243406998e-08 relative error = 1.814939931184952e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000006 y[1] (closed_form) = 1.042381856252636 y[1] (numeric) = 1.042381874579742 absolute error = 1.832710538884896e-08 relative error = 1.758194972304576e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000007 y[1] (closed_form) = 1.045377472128449 y[1] (numeric) = 1.045377489892281 absolute error = 1.776383240503776e-08 relative error = 1.69927446101068e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000007 y[1] (closed_form) = 1.048477921189756 y[1] (numeric) = 1.048477938365426 absolute error = 1.717567066350512e-08 relative error = 1.63815282290495e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000007 y[1] (closed_form) = 1.051683556746739 y[1] (numeric) = 1.051683573308675 absolute error = 1.656193560073405e-08 relative error = 1.574802182128479e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000007 y[1] (closed_form) = 1.054994747465923 y[1] (numeric) = 1.054994763387825 absolute error = 1.592190201904486e-08 relative error = 1.509192539326756e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000007 y[1] (closed_form) = 1.058411877806498 y[1] (numeric) = 1.058411893061297 absolute error = 1.525479897956927e-08 relative error = 1.441291362979034e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000007 y[1] (closed_form) = 1.061935348483729 y[1] (numeric) = 1.061935363043536 absolute error = 1.45598071377151e-08 relative error = 1.371063422882017e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000007 y[1] (closed_form) = 1.065565576961187 y[1] (numeric) = 1.065565590797244 absolute error = 1.383605696680945e-08 relative error = 1.298470715079549e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3700000000000007 y[1] (closed_form) = 1.069302997973717 y[1] (numeric) = 1.069303011056341 absolute error = 1.308262365107282e-08 relative error = 1.223472081894825e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000007 y[1] (closed_form) = 1.073148064083205 y[1] (numeric) = 1.07314807638173 absolute error = 1.229852442108381e-08 relative error = 1.146023072928943e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000007 y[1] (closed_form) = 1.077101246269406 y[1] (numeric) = 1.077101257752121 absolute error = 1.148271455697625e-08 relative error = 1.066075691282245e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000007 y[1] (closed_form) = 1.081163034558304 y[1] (numeric) = 1.081163045192385 absolute error = 1.063408094914564e-08 relative error = 9.835779257371728e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000008 y[1] (closed_form) = 1.085333938690706 y[1] (numeric) = 1.085333948442147 absolute error = 9.751440543936951e-09 relative error = 8.984737504569893e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000008 y[1] (closed_form) = 1.089614488834023 y[1] (numeric) = 1.089614497667554 absolute error = 8.833531017771179e-09 relative error = 8.107024189099931e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000008 y[1] (closed_form) = 1.094005236340475 y[1] (numeric) = 1.094005244219483 absolute error = 7.879008778743923e-09 relative error = 7.20198452166442e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4400000000000008 y[1] (closed_form) = 1.098506754555292 y[1] (numeric) = 1.098506761441732 absolute error = 6.886439862796578e-09 relative error = 6.268909894490738e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4500000000000008 y[1] (closed_form) = 1.103119639678807 y[1] (numeric) = 1.1031196455331 absolute error = 5.854293716467396e-09 relative error = 5.307034256204505e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000008 y[1] (closed_form) = 1.107844511686749 y[1] (numeric) = 1.107844516467684 absolute error = 4.780935203285708e-09 relative error = 4.315529077276821e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000008 y[1] (closed_form) = 1.112682015313499 y[1] (numeric) = 1.112682018978114 absolute error = 3.66461527789852e-09 relative error = 3.293497358152242e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4800000000000008 y[1] (closed_form) = 1.117632821103523 y[1] (numeric) = 1.117632823606986 absolute error = 2.503462548375524e-09 relative error = 2.239968709852012e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000008 y[1] (closed_form) = 1.122697626536821 y[1] (numeric) = 1.122697627832292 absolute error = 1.295471285800431e-09 relative error = 1.153891533374453e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 Finished! diff ( y , x , 1 ) = arcsin ( x + 0.0001 ) ; Iterations = 1000 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.1 %