On Approximate Solution of First-Order Weakly-Singular Volterra Integro-Dynamic Equation on Time Scales

Abstract

Many mathematical formulations of physical phenomena contain integro-dynamic equations. In this paper, we present a new and simple approach to resolve linear weakly-singular Volterra integro-dynamic equations of first-order on any time scales. These equations occur in many applications such as in heat transfer, nuclear reactor dynamics, dynamics of linear viscoelastic materyal with long memory etc. In order to eliminate the singularity of the equation, nabla derivative is used and then transforming the given first-order integro-dynamic equations onto an first-order dynamic equations on time scales. The validity of the method is illustrated with an example. It has been observed that the numerical results efficiently approximate the exact solutions.