Using Invasive Weed Optimization Algorithm with a Padé Approximation to Solve a System of Volterra Integral Equations

Engineering and physics applications are described mathematically as a system of Volterra integral equations (SVIEs). Although many numerical techniques have been considered to solve SVIEs, developing more stable, and efficient algorithms is still challenging. In this work, an algorithm for solving linear and nonlinear system of Volterra integral equations of the second kind is proposed. The Invasive Weed Optimization (IWO) algorithm is combined with Padé approximant expansion. Since the solution is represented as functions of different form, Padé approximation which is fractional expansion is used to obtain results of high accuracy. SVIEs is transformed into an unconstrained optimization problem. Thereafter, the discrete least squares weighted function was estimated to minimize the value of the fitness function. This algorithm is applied to solve a variety of linear and nonlinear examples, and compare their solutions to the exact solutions. The performance of the algorithm provides accurate results in terms of convergence and stability.