A Jacobi dual-Petrov-Galerkin method for solving some odd-order ordinary differential equations

Abstract

A Jacobi dual-Petrov-Galerkin (JDPG) method is introduced and used for solving fully integrated reformulations of third- and fifth-order ordinary differential equations (ODEs) with constant coefficients. The reformulated equation for the J th order ODE involves n -fold indefinite integrals for n=1,.,J. Extension of the JDPG for ODEs with polynomial coefficients is treated using the Jacobi-Gauss-Lobatto quadrature. Numerical results with comparisons are given to confirm the reliability of the proposed method for some constant and polynomial coefficients ODEs. Copyright © 2011 E. H. Doha et al.