Test of the algorithm DETRAP H denotes the current stepsize, used in obtaining the associated solution Y(X) TRUNC is the predicted local error from DETRAP ERROR is the true global error in the numerical solution The initial value problem: y' = 1/(1+x^2) -2 y^2, y(0)=0 True solution: Y(x) = x/(1+x^2) X0 = .000 Y0 = 0.0000000000D+00 XEND = 1.00D+01 H, HMAX, HMIN = 5.00D-01 1.00D+00 1.00D-03 EPS = 5.00D-04 x y(x) h TRUNC IER ERROR .02240 2.2378553039D-02 2.24D-02 5.60D-06 0 5.60D-06 .04479 4.4689891145D-02 2.24D-02 5.59D-06 0 1.12D-05 .06719 6.6867571301D-02 2.24D-02 5.53D-06 0 1.67D-05 .08958 8.8846442936D-02 2.24D-02 5.40D-06 0 2.19D-05 .11198 1.1056330937D-01 2.24D-02 5.22D-06 0 2.69D-05 .13437 1.3195751585D-01 2.24D-02 4.99D-06 0 3.16D-05 .15677 1.5297148641D-01 2.24D-02 4.72D-06 0 3.59D-05 .17916 1.7355120040D-01 2.24D-02 4.41D-06 0 3.97D-05 .20156 1.9364660115D-01 2.24D-02 4.07D-06 0 4.30D-05 .22395 2.1321193164D-01 2.24D-02 3.70D-06 0 4.59D-05 .24635 2.3220599403D-01 2.24D-02 3.31D-06 0 4.82D-05 .26874 2.5059233237D-01 2.24D-02 2.90D-06 0 5.00D-05 .30230 2.7693523474D-01 3.36D-02 6.72D-06 0 5.50D-05 .33586 3.0175801906D-01 3.36D-02 6.22D-06 0 5.86D-05 .36942 3.2500013501D-01 3.36D-02 4.38D-06 0 5.99D-05 .43169 3.6382340006D-01 6.23D-02 -2.70D-06 0 5.33D-05 .53274 4.1504294278D-01 1.01D-01 -1.30D-04 0 -7.51D-05 .57654 4.3279104304D-01 4.38D-02 -1.25D-05 0 -8.20D-05 .62034 4.4804815586D-01 4.38D-02 -1.25D-05 0 -9.08D-05 .66414 4.6096327723D-01 4.38D-02 -1.43D-05 0 -1.00D-04 .70794 4.7170009703D-01 4.38D-02 -1.53D-05 0 -1.10D-04 .75174 4.8043007731D-01 4.38D-02 -1.58D-05 0 -1.19D-04 .79554 4.8732699217D-01 4.38D-02 -1.58D-05 0 -1.27D-04 .83935 4.9256258637D-01 4.38D-02 -1.55D-05 0 -1.34D-04 .88315 4.9630325913D-01 4.38D-02 -1.49D-05 0 -1.39D-04 .92695 4.9870765604D-01 4.38D-02 -1.41D-05 0 -1.43D-04 .97075 4.9992503569D-01 4.38D-02 -1.32D-05 0 -1.45D-04 1.01455 5.0009427508D-01 4.38D-02 -1.22D-05 0 -1.46D-04 1.05835 4.9934338512D-01 4.38D-02 -1.12D-05 0 -1.46D-04 1.10215 4.9778942011D-01 4.38D-02 -1.02D-05 0 -1.45D-04 1.14595 4.9553868115D-01 4.38D-02 -9.27D-06 0 -1.43D-04 1.18975 4.9268712939D-01 4.38D-02 -8.34D-06 0 -1.40D-04 1.23355 4.8932094096D-01 4.38D-02 -7.46D-06 0 -1.36D-04 1.27735 4.8551714937D-01 4.38D-02 -6.65D-06 0 -1.32D-04 1.32115 4.8134433381D-01 4.38D-02 -5.91D-06 0 -1.28D-04 1.38455 4.7477871870D-01 6.34D-02 -1.36D-05 0 -1.27D-04 1.44795 4.6772678927D-01 6.34D-02 -1.30D-05 0 -1.27D-04 1.51135 4.6031658605D-01 6.34D-02 -1.14D-05 0 -1.25D-04 1.57475 4.5265743282D-01 6.34D-02 -9.45D-06 0 -1.22D-04 1.66556 4.4143439989D-01 9.08D-02 -1.66D-05 0 -1.20D-04 1.75637 4.3009436216D-01 9.08D-02 -1.61D-05 0 -1.21D-04 1.84718 4.1878259961D-01 9.08D-02 -1.31D-05 0 -1.18D-04 1.98728 4.0163881279D-01 1.40D-01 -1.59D-05 0 -1.10D-04 2.12738 3.8510326870D-01 1.40D-01 -1.78D-05 0 -1.09D-04 2.36780 3.5846414264D-01 2.40D-01 2.47D-05 0 -5.78D-05 2.84862 3.1206047776D-01 4.81D-01 5.80D-04 0 4.72D-04 3.13912 2.8880912626D-01 2.90D-01 7.66D-05 0 4.02D-04 3.42962 2.6837297333D-01 2.90D-01 4.88D-05 0 3.58D-04 3.72012 2.5036980006D-01 2.90D-01 4.54D-05 0 3.24D-04 4.01062 2.3444962287D-01 2.90D-01 3.94D-05 0 2.95D-04 4.44212 2.1394518472D-01 4.32D-01 1.25D-04 0 3.14D-04 4.87362 1.9655883954D-01 4.32D-01 8.55D-05 0 3.38D-04 5.30512 1.8169406814D-01 4.32D-01 7.20D-05 0 3.35D-04 5.73662 1.6886272178D-01 4.32D-01 5.46D-05 0 3.15D-04 6.43976 1.5126851853D-01 7.03D-01 1.75D-04 0 3.61D-04 7.14289 1.3689903452D-01 7.03D-01 1.20D-04 0 4.09D-04 7.84603 1.2500867803D-01 7.03D-01 9.70D-05 0 4.07D-04 8.84603 1.1121927310D-01 1.00D+00 1.60D-04 1 3.99D-04 9.84603 1.0010974803D-01 1.00D+00 1.09D-04 0 4.17D-04 10.84603 9.1025671471D-02 1.00D+00 8.76D-05 0 3.97D-04 Test #2 of the algorithm DETRAP H denotes the current stepsize, used in obtaining the associated solution Y(X) TRUNC is the predicted local error from DETRAP TRUTRN denotes the true local error ERROR is the true global error in the numerical solution The initial value problem: y' = 1/(1+x^2) -2 y^2, y(0)=0 True solution: Y(x) = x/(1+x^2) X0= .000 Y0= 0.0000000000D+00 XEND= 1.00D+01 H, HMAX, HMIN= 5.00D-01 1.00D+00 1.00D-03 EPS=5.00D-04 x y(x) h TRUNC ERROR TRUTRN .02240 2.2378553039D-02 2.24D-02 5.60D-06 5.60D-06 5.60D-06 .04479 4.4689891145D-02 2.24D-02 5.59D-06 1.12D-05 5.61D-06 .06719 6.6867571301D-02 2.24D-02 5.53D-06 1.67D-05 5.52D-06 .08958 8.8846442936D-02 2.24D-02 5.40D-06 2.19D-05 5.38D-06 .11198 1.1056330937D-01 2.24D-02 5.22D-06 2.69D-05 5.19D-06 .13437 1.3195751585D-01 2.24D-02 4.99D-06 3.16D-05 4.95D-06 .15677 1.5297148641D-01 2.24D-02 4.72D-06 3.59D-05 4.67D-06 .17916 1.7355120040D-01 2.24D-02 4.41D-06 3.97D-05 4.35D-06 .20156 1.9364660115D-01 2.24D-02 4.07D-06 4.30D-05 4.00D-06 .22395 2.1321193164D-01 2.24D-02 3.70D-06 4.59D-05 3.61D-06 .24635 2.3220599403D-01 2.24D-02 3.31D-06 4.82D-05 3.21D-06 .26874 2.5059233237D-01 2.24D-02 2.90D-06 5.00D-05 2.80D-06 .30230 2.7693523474D-01 3.36D-02 6.72D-06 5.50D-05 6.76D-06 .33586 3.0175801906D-01 3.36D-02 6.22D-06 5.86D-05 5.77D-06 .36942 3.2500013501D-01 3.36D-02 4.38D-06 5.99D-05 3.68D-06 .43169 3.6382340006D-01 6.23D-02 -2.70D-06 5.33D-05 -1.67D-06 .53274 4.1504294278D-01 1.01D-01 -1.30D-04 -7.51D-05 -1.21D-04 .57654 4.3279104304D-01 4.38D-02 -1.25D-05 -8.20D-05 -1.22D-05 .62034 4.4804815586D-01 4.38D-02 -1.25D-05 -9.08D-05 -1.50D-05 .66414 4.6096327723D-01 4.38D-02 -1.43D-05 -1.00D-04 -1.65D-05 .70794 4.7170009703D-01 4.38D-02 -1.53D-05 -1.10D-04 -1.75D-05 .75174 4.8043007731D-01 4.38D-02 -1.58D-05 -1.19D-04 -1.78D-05 .79554 4.8732699217D-01 4.38D-02 -1.58D-05 -1.27D-04 -1.77D-05 .83935 4.9256258637D-01 4.38D-02 -1.55D-05 -1.34D-04 -1.72D-05 .88315 4.9630325913D-01 4.38D-02 -1.49D-05 -1.39D-04 -1.64D-05 .92695 4.9870765604D-01 4.38D-02 -1.41D-05 -1.43D-04 -1.55D-05 .97075 4.9992503569D-01 4.38D-02 -1.32D-05 -1.45D-04 -1.44D-05 1.01455 5.0009427508D-01 4.38D-02 -1.22D-05 -1.46D-04 -1.33D-05 1.05835 4.9934338512D-01 4.38D-02 -1.12D-05 -1.46D-04 -1.22D-05 1.10215 4.9778942011D-01 4.38D-02 -1.02D-05 -1.45D-04 -1.10D-05 1.14595 4.9553868115D-01 4.38D-02 -9.27D-06 -1.43D-04 -9.95D-06 1.18975 4.9268712939D-01 4.38D-02 -8.34D-06 -1.40D-04 -8.93D-06 1.23355 4.8932094096D-01 4.38D-02 -7.46D-06 -1.36D-04 -7.97D-06 1.27735 4.8551714937D-01 4.38D-02 -6.65D-06 -1.32D-04 -7.09D-06 1.32115 4.8134433381D-01 4.38D-02 -5.91D-06 -1.28D-04 -6.28D-06 1.38455 4.7477871870D-01 6.34D-02 -1.36D-05 -1.27D-04 -1.34D-05 1.44795 4.6772678927D-01 6.34D-02 -1.30D-05 -1.27D-04 -1.47D-05 1.51135 4.6031658605D-01 6.34D-02 -1.14D-05 -1.25D-04 -1.23D-05 1.57475 4.5265743282D-01 6.34D-02 -9.45D-06 -1.22D-04 -1.01D-05 1.66556 4.4143439989D-01 9.08D-02 -1.66D-05 -1.20D-04 -1.64D-05 1.75637 4.3009436216D-01 9.08D-02 -1.61D-05 -1.21D-04 -1.86D-05 1.84718 4.1878259961D-01 9.08D-02 -1.31D-05 -1.18D-04 -1.40D-05 1.98728 4.0163881279D-01 1.40D-01 -1.59D-05 -1.10D-04 -1.63D-05 2.12738 3.8510326870D-01 1.40D-01 -1.78D-05 -1.09D-04 -2.11D-05 2.36780 3.5846414264D-01 2.40D-01 2.47D-05 -5.78D-05 1.85D-05 2.84862 3.1206047776D-01 4.81D-01 5.80D-04 4.72D-04 4.99D-04 3.13912 2.8880912626D-01 2.90D-01 7.66D-05 4.02D-04 6.90D-05 3.42962 2.6837297333D-01 2.90D-01 4.88D-05 3.58D-04 6.68D-05 3.72012 2.5036980006D-01 2.90D-01 4.54D-05 3.24D-04 5.94D-05 4.01062 2.3444962287D-01 2.90D-01 3.94D-05 2.95D-04 4.99D-05 4.44212 2.1394518472D-01 4.32D-01 1.25D-04 3.14D-04 1.14D-04 4.87362 1.9655883954D-01 4.32D-01 8.55D-05 3.38D-04 1.17D-04 5.30512 1.8169406814D-01 4.32D-01 7.20D-05 3.35D-04 9.15D-05 5.73662 1.6886272178D-01 4.32D-01 5.46D-05 3.15D-04 6.73D-05 6.43976 1.5126851853D-01 7.03D-01 1.75D-04 3.61D-04 1.59D-04 7.14289 1.3689903452D-01 7.03D-01 1.20D-04 4.09D-04 1.68D-04 7.84603 1.2500867803D-01 7.03D-01 9.70D-05 4.07D-04 1.24D-04 8.84603 1.1121927310D-01 1.00D+00 1.60D-04 3.99D-04 1.45D-04 9.84603 1.0010974803D-01 1.00D+00 1.09D-04 4.17D-04 1.55D-04 10.84603 9.1025671471D-02 1.00D+00 8.76D-05 3.97D-04 1.12D-04