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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 \(n = 1, \dots, J\). 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.

65L05 Numerical methods for initial value problems
34A30 Linear ordinary differential equations and systems, general
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
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