Open AccessSpectral Shifted Jacobi Tau and Collocation Methods for Solving Fifth‐Order Boundary Value Problems
Author(s) -
A. H. Bhrawy,
A. S. Alofi,
S. I. El-Soubhy
Publication year - 2011
Publication title -
abstract and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.228
H-Index - 56
eISSN - 1687-0409
pISSN - 1085-3375
DOI - 10.1155/2011/823273
Subject(s) - mathematics , collocation (remote sensing) , boundary value problem , algebraic equation , collocation method , orthogonal collocation , jacobi polynomials , jacobi method , order (exchange) , algebraic number , spectral method , boundary (topology) , mathematical analysis , nonlinear system , differential equation , ordinary differential equation , orthogonal polynomials , computer science , physics , finance , quantum mechanics , machine learning , economics
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
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