Behaviour of solutions of the volterra integro-differential equations using numerical methods

Abstract

This paper is interested in solving Volterra integro-differential equation with associated initial condition. The Implicit Euler method was used to approximate the derivatives and the Explicit Euler method to approximate the integral as the numerical schemes. The result shows that the long term qualitative behaviour of the solutions obtained from the schemes with different choices of λ and step-sizes of h values are independent of the parameters. Finally, the comparison of the exact solution of the original integro-differential equation (1) with the numerical schemes shows that the qualitative behaviour of the solutions are all the same.