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Numerical solution of nonlinear Volterra-Fredholm-Hammerstein integral equations via collocation method based on radial basis functions. (English) Zbl 1244.65245

Summary: A numerical technique based on the spectral method is presented for the solution of nonlinear Volterra-Fredholm-Hammerstein integral equations. This method is a combination of collocation method and radial basis functions (RBFs) with the differentiation process, using zeros of the shifted Legendre polynomial as the collocation points. Different applications of RBFs are used for this purpose. The integral involved in the formulation of the problems is approximated based on Legendre-Gauss-Lobatto integration rule. The results of numerical experiments are compared with the analytical solution in illustrative examples to confirm the accuracy and efficiency of the presented scheme.

MSC:

65R20 Numerical methods for integral equations
45D05 Volterra integral equations
45B05 Fredholm integral equations
45G10 Other nonlinear integral equations

Software:

Matlab
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Full Text: DOI

References:

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