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Spectral Shifted Jacobi Tau and Collocation Methods for Solving Fifth-Order Boundary Value Problems

Author

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  • A. H. Bhrawy
  • A. S. Alofi
  • S. I. El-Soubhy

Abstract

We have presented an efficient spectral algorithm based on shifted Jacobi tau method of linear fifth-order two-point boundary value problems (BVPs). An approach that is implementing the shifted Jacobi tau method in combination with the shifted Jacobi collocation technique is introduced for the numerical solution of fifth-order differential equations with variable coefficients. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplify the problem. Shifted Jacobi collocation method is developed for solving nonlinear fifth-order BVPs. Numerical examples are performed to show the validity and applicability of the techniques. A comparison has been made with the existing results. The method is easy to implement and gives very accurate results.

Suggested Citation

  • A. H. Bhrawy & A. S. Alofi & S. I. El-Soubhy, 2011. "Spectral Shifted Jacobi Tau and Collocation Methods for Solving Fifth-Order Boundary Value Problems," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-14, July.
    • Handle: RePEc:hin:jnlaaa:823273
    DOI: 10.1155/2011/823273
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    Cited by:

    1. Tafakkori–Bafghi, M. & Loghmani, G.B. & Heydari, M., 2022. "Numerical solution of two-point nonlinear boundary value problems via Legendre–Picard iteration method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 199(C), pages 133-159.

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