An Efficient Numerical Approach Based on the Adomian Chebyshev Decomposition Method for Two-Point Boundary Value Problems

Authors

  • A. AL-Refaidi University of Jeddah
  • N. ALZaid Department of Mathematics and statistics, Faculty of Science, University of Jeddah
  • Huda Bakodah University of Jeddah
  • M. AL-Mazmumy Department of Mathematics and statistics, Faculty of Science, University of Jeddah

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i3.5232

Keywords:

Boundary Value Problems (BVPs);Adomian Decomposition Method (ADM); Adomian Chebyshev Decomposition Method (ACDM), Chebyshev polynomials, Dirichlet conditions.

Abstract

The current manuscript devises an efficient numerical method for solving two-point nonhomogeneous Boundary Value Problems (BVPs) with Dirichlet conditions. The method is based on the application of the celebrated Adomian Decomposition Method (ADM) and, the Chebyshev polynomials. This method which refers to ”Adomian Chebyshev Decomposition Method” (ACDM) is further proved to be a robust numerical method as the associated nonhomogeneous terms are successfully reinstated with a reliable Chebyshev series. Lastly, a comparative study between the acquired numerical results and the existing exact solutions of the test problems has been established to demonstrate the salient features of the devised method

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Published

2024-07-31

Issue

Vol. 17 No. 3: (July 2024)

Section

Nonlinear Analysis

License

Copyright (c) 2024 European Journal of Pure and Applied Mathematics

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How to Cite

An Efficient Numerical Approach Based on the Adomian Chebyshev Decomposition Method for Two-Point Boundary Value Problems. (2024). European Journal of Pure and Applied Mathematics, 17(3), 1497-1515. https://doi.org/10.29020/nybg.ejpam.v17i3.5232