A Jacobi Dual-Petrov-Galerkin Method for Solving Some Odd-Order Ordinary Differential Equations

الملخص EN

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 Jth 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.