Numerical Solutions of Volterra Integral Equations Using Laguerre Polynomials

We solve numerically Volterra integral equations, of first and second kind with regular and singular kernels, by the well known Galerkin weighted residual method. For this, we derive a simple and efficient matrix formulation using Laguerre polynomials as trial functions. Several numerical examples are tested. The approximate solutions of some examples coincide with the exact solutions on using a very few Laguerre polynomials. The approximate results, obtained by the present method, confirm the convergence of numerical solutions and are compared with the existing methods available in the literature.Keywords: Volterra integral equations; Galerkin method; Laguerre polynomials.