On the weight function for the Chebyshev equation of the first kind by the Adomian decomposition method

Abstract: In this paper, we study the use of the Adomian decomposition method (ADM) to solve the Chebyshev equation of the first kind. We show that the ADM can be used to obtain a series solution for the equation, and that the weight function for the series can be chosen to improve the accuracy of the solution. We studied the weight of Chebyshev differential equations using the Adomian decomposition method and show that the ADM is a more efficient and accurate method. Keywords: Adomian decomposition method, Chebyshev equation from first kind, weight function, Chebyshev polynomial. Title: On the weight function for the Chebyshev equation of the first kind by the Adomian decomposition method Author: Mohammed Ali Qasem Mohsen‚ Arafa Abdalrahim Ahmed Dawood International Journal of Mathematics and Physical Sciences Research ISSN 2348-5736 (Online) Vol. 13, Issue 1, April 2025 - September 2025 Page No: 66-69 Research Publish Journals Website: www.researchpublish.com Published Date: 23-May-2025 DOI: https://doi.org/10.5281/zenodo.15494954 Paper Download Link (Source) https://www.researchpublish.com/papers/on-the-weight-function-for-the-chebyshev-equation-of-the-first-kind-by-the-adomian-decomposition-method