Series Solution of Weakly-Singular Kernel Volterra Integro-Differential Equations by the Combined Laplace-Adomian Method

To solve the weakly-singular Volterra integro-differential equations, the combined method of the Laplace Transform Method and the Adomian Decomposition Method is used. As a result, series solutions of the equations are constructed. In order to explore the rapid decay of the equations, the pade approximation is used. The results present validity and great potential of the method as a powerful algorithm in order to present series solutions for singular kind of differential equations.