The Numerical Solution of Volterra Integral Equations of the First Kind Using Hermite Polynomials via the Galerkin’s Residual Method
Abstract
In this paper, the method for solving Volterra integral equations of the first kind with weakly singular kernels using the Hermite polynomials is presented. The procedure resulted in the construction of systems of algebraic equations, solving these systems of algebraic equations an approximate solution ?( ) is obtained numerically; Illustrative examples are included to demonstrate the simplicity and applicability of the method. Once the approximate solution coincides with the exact solution for any particular value of , further evaluations can only give an approximate solution. The volume of work involve in this method is much easier than most of the existing methods contained in the literature.
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