Barycentric rational method for solving biharmonic equation by depression of order

Abstract

Two-dimensional biharmonic boundary-value problems are considered by the linear barycentric rational method, the unknown function was approximated by the barycentric rational function. For the biharmonic equation, we change the biharmonic equation into the two Poisson equations by depression of order. The linear equations of discrete the biharmonic equation was changed into matrix form. For the basis of barycentric rational function, we present the convergence rate of linear barycentric rational method for biharmonic equation by depression of order. At last, several numerical examples are provided to validate the theoretical analysis. KEYWORDS barycentric rational function, barycentric rational method, biharmonic equation, depression of order, matrix form where Ω = [a, b] × [c, d] and f (x, y), g(x, y), h(x, y) are consistent on Ω. Biharmonic equation is widely used in electrostatics, mechanical engineering and theoretical physics and so on. There are lots of methods to solve biharmonic equation such as finite difference method, finite element method, boundary element method and spectral method and so on.

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