Single-Term Walsh Series method for systems of linear Volterra integral equations of the second kind

摘要

This paper generalizes Single-Term Walsh Series method for solving systems of linear Volterra integral equations of the second kind. Using the properties of Walsh functions, this method reduces these types of equations to a linear system of algebraic equations. In addition, this method (i) does not require any operational matrices, (ii) needs less computational effort, (iii) gives both piecewise constant and discrete solution, (iv) yields good agreement with exact solutions. Convergence results and error analysis are discussed. Numerical examples are presented to illustrate the computational efficiency of the method.