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Abstract
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In this paper, amethod 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.
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