Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method. (English) Zbl 1061.65145

Summary: We present a Taylor-series expansion method for a class of Volterra integral equations of second kind with smooth or weakly singular kernels. This method use Taylor-series approximation method for integral equation and transform the integral equation to an \(n\)th order, linear differential equation. Boundary conditions for differential equation produce in easy way. This method gives an approximate simple and closed form solution for integral equation. Some numerical examples to illustrate the accuracy of method.


65R20 Numerical methods for integral equations
45D05 Volterra integral equations
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
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