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An extension of the Legendre-Galerkin method for solving sixth-order differential equations with variable polynomial coefficients. (English) Zbl 1264.65121
Summary: We extend the application of Legendre-Galerkin algorithms for sixth-order elliptic problems with constant coefficients to sixth-order elliptic equations with variable polynomial coefficients. The complexities of the algorithm are O(N) operations for a one-dimensional domain with (N-5) unknowns. An efficient and accurate direct solution for algorithms based on the Legendre-Galerkin approximations developed for the two-dimensional sixth-order elliptic equations with variable coefficients relies upon a tensor product process. The proposed Legendre-Galerkin method for solving variable coefficients problem is more efficient than pseudospectral method. Numerical examples are considered aiming to demonstrate the validity and applicability of the proposed techniques.
MSC:
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE