## 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:

 65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
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### References:

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