Numerical solution of a type of weakly singular nonlinear Volterra integral equation by Tau Method
الموضوعات :H. Laeli Dastjerdi 1 , M. Nili Ahmadabadi 2
1 - Department of Mathematics, Najafabad Branch, Islamic Azad University, Najafabad, Iran
2 - Department of Mathematics, Najafabad Branch, Islamic Azad University, Najafabad, Iran
الکلمات المفتاحية: Nonlinear Equations, Lighthill equation, Volterra integral equations, Tau method, Weakly singular,
ملخص المقالة :
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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