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Efficient spectral-Petrov-Galerkin methods for the integrated forms of third- and fifth-order elliptic differential equations using general parameters generalized Jacobi polynomials. (English) Zbl 1242.65148
Summary: This article analyzes some algorithms for solving numerically the integrated forms of third- and fifth-order differential equations in one variable subject to homogeneous and nonhomogeneous boundary conditions using a dual Petrov-Galerkin method. Two new families of general parameters generalized Jacobi polynomials are introduced and used for this purpose. Numerical results indicating the high accuracy and effectiveness of the proposed algorithms are presented.
MSC:
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
34B05Linear boundary value problems for ODE
65L10Boundary value problems for ODE (numerical methods)
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