A new computational algorithm for the solution of second order initial value problems
in ordinary differential equations
Publié en ligne: 03 oct. 2018
Pages: 167 - 174
Reçu: 09 mars 2018
Accepté: 15 mai 2018
© 2018 P.K. Pandey, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.
Maximum absolute error in y(x) = sin2(x2$\begin{array}{}
\displaystyle
\frac{x}{2}
\end{array}$) and y′(x) for Example 5.4.
MAE | N |
---|
|
---|
128 | 256 | 512 | 1024 | 2048 | 4096 | 8192 |
---|
y | .3083482(-1) | .2080867(-1) | .1396590(-1) | .9322166(-2) | .6191766(-2) | .4095947(-2) | .2701349(-2) |
y′ | .2283364(-2) | .1416236(-2) | .8000433(-3) | .4311204(-3) | .2279877(-3) | .1192688(-3) | .6163130(-4) |
Maximum absolute error in y(x) = e(−20x)$\begin{array}{}
\displaystyle
e^{(\frac{-20}{x})}
\end{array}$ and y′(x) for Example 5.1.
MAE | N |
---|
|
---|
64 | 128 | 256 | 512 | 1024 | 2048 | 4096 |
---|
y | .5621729(-3) | .2748708(-3) | .1313720(-3) | .5965512(-4) | .2474944(-4) | .1009797(-4) | .4115111(-5) |
y′ | .5267575(-6) | .1289518(-6) | .3187597(-7) | .7879862(-8) | .1913576(-8) | .5345364(-9) | .1852914(-9) |
Maximum absolute error in y(x) = (1 + x)–1 and y′(x) for Example 5.3.
MAE | N |
---|
|
---|
128 | 256 | 512 | 1024 | 2048 | 4096 | 8192 |
---|
y | .1363998(-1) | .7091403(-2) | .3645122(-2) | .1860261(-2) | .9453296(-3) | .4789233(-3) | .2411603(-3) |
y′ | .6387859(-2) | .3583610(-2) | .1952946(-2) | .1042857(-2) | .5497336(-3) | .2868771(-3) | .1467168(-3) |
Maximum absolute error in y(x) = (1 + x)–2 and y′(x) for Example 5.2.
MAE | N |
---|
|
---|
128 | 256 | 512 | 1024 | 2048 | 4096 | 8192 |
---|
y | .9100055(-2) | .5043587(-2) | .2747672(-2) | .1475068(-2) | .7822510(-3) | .4106779(-3) | .2136840(-3) |
y′ | .1660321(-1) | .8981451(-2) | .4802107(-2) | .2541303(-2) | .1330271(-2) | .6887614(-3) | .3566145(-3) |