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Some Algorithms for Solving Third‐Order Boundary Value Problems Using Novel Operational Matrices of Generalized Jacobi Polynomials

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  • W. M. Abd-Elhameed

Abstract

The main aim of this research article is to develop two new algorithms for handling linear and nonlinear third‐order boundary value problems. For this purpose, a novel operational matrix of derivatives of certain nonsymmetric generalized Jacobi polynomials is established. The suggested algorithms are built on utilizing the Galerkin and collocation spectral methods. Moreover, the principle idea behind these algorithms is based on converting the boundary value problems governed by their boundary conditions into systems of linear or nonlinear algebraic equations which can be efficiently solved by suitable solvers. We support our algorithms by a careful investigation of the convergence analysis of the suggested nonsymmetric generalized Jacobi expansion. Some illustrative examples are given for the sake of indicating the high accuracy and efficiency of the two proposed algorithms.

Suggested Citation

  • W. M. Abd-Elhameed, 2015. "Some Algorithms for Solving Third‐Order Boundary Value Problems Using Novel Operational Matrices of Generalized Jacobi Polynomials," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).
    • Handle: RePEc:wly:jnlaaa:v:2015:y:2015:i:1:n:672703
    DOI: 10.1155/2015/672703
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    References listed on IDEAS

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    1. W. M. Abd-Elhameed & E. H. Doha & Y. H. Youssri, 2013. "New Wavelets Collocation Method for Solving Second-Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth Kinds," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, October.
    2. W. M. Abd-Elhameed & E. H. Doha & Y. H. Youssri, 2013. "New Wavelets Collocation Method for Solving Second‐Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth Kinds," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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