A Jacobi-Jacobi dual-Petrov-Galerkin method for third- and fifth-order differential equations

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Date

2011

Journal Title

Journal ISSN

Volume Title

Type

Article

Publisher

PERGAMON-ELSEVIER SCIENCE LTD

Series Info

MATHEMATICAL AND COMPUTER MODELLING;Volume: 53 Issue: 9-10 Pages: 1820-1832

Abstract

his paper analyzes a method for solving the third-and fifth-order differential equations with constant coefficients using a Jacobi dual-Petrov-Galerkin method, which is more reasonable than the standard Galerkin one. The spatial approximation is based on Jacobi polynomials P-n((alpha,beta)) with alpha,beta is an element of (-1,infinity) and n is the polynomial degree. By choosing appropriate base functions, the resulting system is sparse and the method can be implemented efficiently. A Jacobi-Jacobi dual-Petrov-Galerkin method for the differential equations with variable coefficients is developed. This method is based on the Petrov-Galerkin variational form of one Jacobi polynomial class, but the variable coefficients and the right-hand terms are treated by using the Gauss-Lobatto quadrature form of another Jacobi class. Numerical results illustrate the theory and constitute a convincing argument for the feasibility of the proposed numerical methods. (C) 2011 Elsevier Ltd. All rights reserved.

Description

Accession Number: WOS:000287729700024

Keywords

October University for University for Petrov-Galerkin method, Jacobi collocation method, Jacobi polynomials, Jacobi-Gauss-Lobatto quadrature, Fast Fourier transform, Jacobi-Jacobi Galerkin method

Citation

Cited References in Web of Science Core Collection: 32