<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this article, we propose a new computational method for second order initial value problems in
ordinary differential equations. The algorithm developed is based on a local representation of theoretical solution of the second order initial value problem by a non-linear interpolating function. Numerical examples are solved to ensure the computational performance of the algorithm for both linear and non-linear initial value problems. From the results we obtained, the algorithm can be said computationally efficient and effective.</p></abstract>

In this article, we propose a new computational method for second order initial value problems in
ordinary differential equations. The algorithm developed is based on a local representation of theoretical solution of the second order initial value problem by a non-linear interpolating function. Numerical examples are solved to ensure the computational performance of the algorithm for both linear and non-linear initial value problems. From the results we obtained, the algorithm can be said computationally efficient and effective.

A new computational algorithm for the solution of second order initial value problems
in ordinary differential equations

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

In this article, we propose a new computational method for second order initial value problems in
ordinary differential equations. The algorithm developed is...

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)

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)

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)

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)

A new computational algorithm for the solution of second order initial value problems in ordinary differential equations

Published Online: Oct 03, 2018

Page range: 167 - 174

Received: Mar 09, 2018

Accepted: May 15, 2018

DOI: https://doi.org/10.21042/AMNS.2018.1.00013

Keywords
Absolute Stability, Finite difference approximations, Initial Value Problems, Maximum Absolute Error, Nonlinear IVP

© 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.

Maximum absolute error in y(x) = e(−20x)$\begin{array}{} \displaystyle e^{(\frac{-20}{x})} \end{array}$ and y′(x) for Example 5.1.

Maximum absolute error in y(x) = (1 + x)–1 and y′(x) for Example 5.3.

Maximum absolute error in y(x) = (1 + x)–2 and y′(x) for Example 5.2.

A new computational algorithm for the solution of second order initial value problems in ordinary differential equations

Published Online: Oct 03, 2018

Page range: 167 - 174

Received: Mar 09, 2018

Accepted: May 15, 2018

DOI: https://doi.org/10.21042/AMNS.2018.1.00013

KeywordsAbsolute Stability, Finite difference approximations, Initial Value Problems, Maximum Absolute Error, Nonlinear IVP

© 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.

Maximum absolute error in y(x) = e(−20x)$\begin{array}{} \displaystyle e^{(\frac{-20}{x})} \end{array}$ and y′(x) for Example 5.1.

Maximum absolute error in y(x) = (1 + x)–1 and y′(x) for Example 5.3.

Maximum absolute error in y(x) = (1 + x)–2 and y′(x) for Example 5.2.

Keywords
Absolute Stability, Finite difference approximations, Initial Value Problems, Maximum Absolute Error, Nonlinear IVP