Laeli Dastjerdi, H., Nili Ahmadabadi, M. (2018). Numerical solution of a type of weakly singular nonlinear Volterra integral equation by Tau Method. Journal of Linear and Topological Algebra (JLTA), 07(02), 75-85.

H. Laeli Dastjerdi; M. Nili Ahmadabadi. "Numerical solution of a type of weakly singular nonlinear Volterra integral equation by Tau Method". Journal of Linear and Topological Algebra (JLTA), 07, 02, 2018, 75-85.

Laeli Dastjerdi, H., Nili Ahmadabadi, M. (2018). 'Numerical solution of a type of weakly singular nonlinear Volterra integral equation by Tau Method', Journal of Linear and Topological Algebra (JLTA), 07(02), pp. 75-85.

Laeli Dastjerdi, H., Nili Ahmadabadi, M. Numerical solution of a type of weakly singular nonlinear Volterra integral equation by Tau Method. Journal of Linear and Topological Algebra (JLTA), 2018; 07(02): 75-85.

Numerical solution of a type of weakly singular nonlinear Volterra integral equation by Tau Method

^{}Department of Mathematics, Najafabad Branch, Islamic Azad University, Najafabad, Iran

Abstract

In this paper, a matrix based method is considered for the solution of a class of nonlinear Volterra integral equations with a kernel of the general form $s^{\beta}(t-s)^{-\alpha}G(y(s))$ based on the Tau method. In this method, a transformation of the independent variable is first introduced in order to obtain a new equation with smoother solution. Error analysis of this method is also presented. Some numerical examples are provided to illustrate the accuracy and computational efficiency of the method.

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