On the performance of Lucas polynomials on linear and nonlinear Volterra integral equations of the second kind

Abstract

In this article, we consider Lucas series for 𝑁 = 2, 5, 6 in numerical solutions of linear and nonlinear Volterra integral equations of the second kind. The series is used to transform the equation into a system of nonlinear algebraic equations, and the unknown parameters are determined. The application of this method has shown that the Lucas series is a powerful and active candidate that can be used to approximate the solution of linear and nonlinear Volterra integral equations of the second kind. The method gave a good performance, as can be seen from the four sample problems considered. The numerical results reveal computational efficiency of the method and it is also seen to be highly accurate and converge to the exact solution in some cases. Approximate and exact solutions are plotted to further confirm the accuracy of the method.

Keywords

• algorithm
• convergent
• volterra integral equations
• second kind
• linear and nonlinear