Numerical Solution of Linear Volterra Integral Equation Systems of Second Kind by Radial Basis Functions

Abstract

In this paper we propose an approximation method for solving second kind Volterra integral equation systems by radial basis functions. It is based on the minimization of a suitable functional in a discrete space generated by compactly supported radial basis functions of Wendland type. We prove two convergence results, and we highlight this because most recent published papers in the literature do not include any. We present some numerical examples in order to show and justify the validity of the proposed method. Our proposed technique gives an acceptable accuracy with small use of the data, resulting also in a low computational cost.

Approximate solution to solve non-linear integro-differential type defined using boundary value problems

“…The accuracy of the approximation depends on the type of equation, the approximations used, and the number of iterations. Nonlinear Volterra-Fredholm integro-differential equations have been used in many engineering applications such as robotics and automation, control systems, and signal processing [2][3][4][5][6].…”