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A Jacobi dual-Petrov-Galerkin method for solving some odd-order ordinary differential equations. (English) Zbl 1216.65086
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 $n=1,\cdots ,J$. 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.
MSC:
 65L05 Initial value problems for ODE (numerical methods) 34A30 Linear ODE and systems, general 65L60 Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE