Single-Term Walsh Series Approach for the System of Linear and Non-linear Volterra Integral Equations of First Kind

Abstract

In this article, we apply the Single Term Walsh Series (STWS) method to solve the systems of Volterra integral equations of first kind (SVIEF). Because of the ill-posedness of the first kind problem, the SVIEF is converted into system of Volterra integral equations of second kind (SVIES). The STWS method for the SVIES with variable coefficient is presented. Numerical examples for linear and non-linear problems are experimented to show the efficiency and simplicity of the STWS method. The obtained numerical solutions (results) have been compared with the existing method.