An Extension of the Legendre-Galerkin Method for Solving Sixth-Order Differential Equations with Variable Polynomial Coefficients

A. H. Bhrawy, A. S. Alofi and S. I. El-Soubhy

Mathematical Problems in Engineering, 2012, vol. 2012, 1-13

Abstract:

We extend the application of Legendre-Galerkin algorithms for sixth-order elliptic problems with constant coefficients to sixth-order elliptic equations with variable polynomial coefficients. The complexities of the algorithm are O(N) operations for a one-dimensional domain with ( ) unknowns. An efficient and accurate direct solution for algorithms based on the Legendre-Galerkin approximations developed for the two-dimensional sixth-order elliptic equations with variable coefficients relies upon a tensor product process. The proposed Legendre-Galerkin method for solving variable coefficients problem is more efficient than pseudospectral method. Numerical examples are considered aiming to demonstrate the validity and applicability of the proposed techniques.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:896575

DOI: 10.1155/2012/896575

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