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

Document Type: Research Articles

Authors

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.

Keywords


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