Theory and Computations for the System of Integral Equations via the use of Optimal Auxiliary Function Method

Abstract

This paper extends the application of Optimal Auxiliary Function Method (OAFM) to the system of integral equations. The system of Volterra integral equations of second kind are taken as test examples. The results obtained by proposed method are compared with different methods i.e., Biorthogonal systems in a Banach space Fixed point, the implicit Trapezoidal rule in conjunction with Newton's method, and Relaxed Monte Carlo method (RMCM). The results revealed that OAFM is more efficient, simple to apply, and fast convergent. The auxiliary functions used in the method control its convergence. The values of arbitrary constants involved in the auxiliary functions are calculated optimally using the method of least square