Nazari, J., Almasieh, H. (2014). A meshless technique for nonlinear Volterra-Fredholm integral equations via hybrid of radial basis functions. Theory of Approximation and Applications, 10(2), 43-59.

Jinoos Nazari; Homa Almasieh. "A meshless technique for nonlinear Volterra-Fredholm integral equations via hybrid of radial basis functions". Theory of Approximation and Applications, 10, 2, 2014, 43-59.

Nazari, J., Almasieh, H. (2014). 'A meshless technique for nonlinear Volterra-Fredholm integral equations via hybrid of radial basis functions', Theory of Approximation and Applications, 10(2), pp. 43-59.

Nazari, J., Almasieh, H. A meshless technique for nonlinear Volterra-Fredholm integral equations via hybrid of radial basis functions. Theory of Approximation and Applications, 2014; 10(2): 43-59.

A meshless technique for nonlinear Volterra-Fredholm integral equations via hybrid of radial basis functions

^{1}Department of Mathematics, Islamic Azad University, Khorasgan(Isfahan) Branch

^{2}Department of Mathematics, Khorasgan (Isfahan) Branch, Islamic Azad University

Abstract

In this paper, an effective technique is proposed to determine the numerical solution of nonlinear Volterra-Fredholm integral equations (VFIEs) which is based on interpolation by the hybrid of radial basis functions (RBFs) including both inverse multiquadrics (IMQs), hyperbolic secant (Sechs) and strictly positive definite functions. Zeros of the shifted Legendre polynomial are used as the collocation points to set up the nonlinear systems. The integrals involved in the formulation of the problems are approximated based on Legendre-Gauss-Lobatto integration rule. This technique is so convenience to implement and yields very accurate results compared with the other basis. In addition a convergence theorem is proved to show the stability of this technique. Illustrated examples are included to confirm the validity and applicability of the proposed method. The comparison of the errors is implemented by the other methods in references using both inverse multiquadrics (IMQs), hyperbolic secant (Sechs) and strictly positive definite functions.

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