Spectral Solutions of System of Volterra Integro-Differential Equations and Their Error Analysis

Abstract

This paper presents the numerical solutions of a system of Linear Volterra Integro-Differential Equations (LVIDEs) using spectral collocation method. A general equation consisting of a system of LVIDEs each with mth order derivative is formulated and seven different cases of this general equation are analysed for their spectral solutions. It is shown that, the complex mathematical form of a system of LVIDEs can be handled with great ease with the present Spectral method. The importance of this paper is the analysis of solutions using three different basis functions such as Chebyshev, Legendre and Jacobi Polynomials which no one has attempted so far. The convergence of the solution for different values of collocation points and various other results are computed and they are presented in the form of tables and figures. Lastly, a new example is ventured considering a system of three LVIDEs in three unknown functions each having third order derivative. We show that spectral method gives accurate results for these equations as well. Hence, it is concluded that a system of LVIDEs can also be handled well by the present spectral collocation method.