A Jacobi dual-Petrov-Galerkin method for solving some odd-order ordinary differential equations (Q535998)

Summary: 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 \(n = 1, \dots, J\). The extension of the JDPG method to ODEs with polynomial coefficients is treated using 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.