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Extrapolation of the Galerkin solution for two-dimensional nonlinear Fredholm integral equations with orthogonal basis of Boubaker polynomials. (English) Zbl 1499.65759

Summary: In this paper, a method for finding an approximate Galerkin solution of two-dimensional nonlinear Fredholm integral equations using orthogonal base 4n-order Boubaker polynomials is discussed. The properties of two-dimensional shifted Boubaker functions are presented. For an iterated discrete Galerkin method, in addition to calculating the asymptotic expansion error, also, if the solution of the integral equation is continuously differentiable function, this asymptotic extension can be extended to higher powers of the discrete parameters. Furthermore, the use of extrapolation formulas contributes to increasing the convergence rate of this expansion. Numerical examples demonstrate that how extrapolation imputes a significant enlargement of accuracy, moreover, quicker convergence.

MSC:

65R20 Numerical methods for integral equations
31A10 Integral representations, integral operators, integral equations methods in two dimensions
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