# A SEMI-ANALYTIC DECOMPOSITION METHOD WITH SHIFTED CHEBYSHEV POLYNOMIAL OF FIRST KIND FOR SOLVING SOME CLASS OF SECOND ORDER NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS

## Keywords:

orthogonal polynomial, Van der pol’s equations, Duffing’s equations, ordinary differential equation## Abstract

A semi-analytic decomposition method for the solution of non-linear initial value problems based on a reliable decomposition algorithm with shifted Chebyshev orthogonal polynomial of first kind is presented to obtain an approximated solution of some class of second order nonlinear ordinary differential equations. The proposed method surmounts the use of special polynomials. Numerical tests are carried out on Duffing and Van der pol differential oscillatory equations. The results obtained in this paper demonstrate reliability, efficiency and accuracy of the new algorithm when compared to other known methods in the literature.

Keywords: Decomposition method, shifted Chebyshev polynomial,

**Views | Downloads:**43 / 13

## Downloads

## References

Adomain, G. Solving Frontier Problems of Physics, the Decomposition Method, Kluwer Academic Publisher, Boston, USA,1994

Daftardar –Gejji, V, Jafari, H (2006); An Iterative method for solving nonlinear functional equations. Journal of Analysis and Applications, 316, 753-763

Wazwaz, A. M (1999); A Modification of Adomian Decomposition Method. Applied Mathematics Computation, 102, 77-86

Wazwaz, A. M (2000); A new algorithm calculating Adomian polynomials for nonlinear operators. Applied Mathematics Computation, 111, 53-69

Pourdavish, A. (2006); A reliable symbolic implementation of algorithm for calculating Adomain polynomials Applied Mathematics Computation, 175, 545-550

Osilagun, J. A, Taiwo, O. A. (2014); Solving Abelian Differential Equation by iterative decomposition method, Journal of the Nigerian Association of Mathematical Physics, 26, 46-49

Kreyzig, E, Introductory functional analysis with applications, John Wiley & Sons, New York, USA, 1978

Hosseini, M. M. (2006); Adomain decomposition method with chebshev polynomials. Applied Mathematics Computation, 175, 1655-1693.

Yucheng, L. (2009); Adomian decomposition method with orthogonal polynomial; Legendre polynomials. Mathematical and Computer Modeling, 49, 1268-1273.

Wei-Chung, T. Chao-Kuang C (2009); Adomian decomposition method by Legendre polynomials. Chaos, solutions and Fractals, 39, 2093-2101.

Wazwaz, A. M., El-Sayed, S. M. (2001); A new modification of the Adomian decomposition method for linear and nonlinear operators. Applied Mathematics Computation, 122, 393-405.

Hosseini, M. M. (2006); Adomian decomposition method with chebyshev polynomials. Applied mathematical and computation, 175, 1685-169

## Downloads

## Published

## Issue

## Section

## License

Copyright (c) 2024 The Transactions of the Nigerian Association of Mathematical Physics

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

## How to Cite

*The Transactions of the Nigerian Association of Mathematical Physics*,

*17*, 83 –88. https://nampjournals.org.ng/index.php/tnamp/article/view/207