Abstract—Lubich convolution quadrature formulas have the fundamental property of not using explicitly the expression of the kernel of the integral equation they are applied to, which is instead replaced by that of its Laplace transform, usually given by a simple analytic function. In this paper, the Lubichcollocation procedure was successfully employed to reduce a system of nonlinear Volterra integral equations with convolution kernels to a system of algebraic equations. An example is considered to illustrate the ability of the proposed method.

Index Terms—Nonlinear integral equation, Convolution kernel, Lubich quadrature.

R. Zolfaghari is with the Department of Computer Science in Salman Farsi University of Kazerun, Iran (e-mail: zolfaghari@kazerunsfu.ac.ir).

 

Cite: Reza Zolfaghari, "Lubich-Collocation Method for Solving a System of Nonlinear Integral Equations of Convolution Type," International Journal of Applied Physics and Mathematics vol. 4, no. 2, pp. 121-125, 2014.