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

Author

Listed:
  • 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, John Wiley & Sons, vol. 2011(1).
    • Handle: RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:823273
    DOI: 10.1155/2011/823273
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    References listed on IDEAS

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    1. E. H. Doha & A. H. Bhrawy & R. M. Hafez, 2011. "A Jacobi Dual-Petrov-Galerkin Method for Solving Some Odd-Order Ordinary Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-21, April.
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    Cited by:

    1. A. H. Bhrawy & M. A. Alghamdi, 2012. "Numerical Solutions of Odd Order Linear and Nonlinear Initial Value Problems Using a Shifted Jacobi Spectral Approximations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Ali H. Bhrawy & M. M. Al-Shomrani, 2012. "A Jacobi Dual‐Petrov Galerkin‐Jacobi Collocation Method for Solving Korteweg‐de Vries Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. 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).
    4. E. H. Doha & W. M. Abd-Elhameed, 2012. "Efficient Solutions of Multidimensional Sixth‐Order Boundary Value Problems Using Symmetric Generalized Jacobi‐Galerkin Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    5. 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.
    6. A. H. Bhrawy & M. M. Tharwat & A. Al-Fhaid, 2012. "Numerical Algorithms for Computing Eigenvalues of Discontinuous Dirac System Using Sinc‐Gaussian Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).

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