Abstract
This paper investigates the numerical solution of systems of nonlinear Fredholm integro-differential equations of the second kind using the Quintic B-spline method. These equations are significant in various scientific fields, including fluid dynamics, biological models, and chemical kinetics, due to their complexity and widespread applications. Traditional analytical solutions are often impractical; hence, efficient numerical methods are essential. We extend the use of Quintic B-splines, previously applied to other types of integro-differential equations, to these systems. The method is described in detail, including the formulation of the integro-differential equations, the construction of Quintic B-spline interpolants, and the application of LU matrix factorization to solve the resulting system of equations. We present three numerical examples to demonstrate the accuracy and efficiency of the proposed method, comparing theoretical and numerical results using the maximum absolute error and least square error norms. The results show that the Quintic B-spline method provides a reliable and accurate approach for solving complex integro-differential equations.
Keywords: Quintic B-spline, Nonlinear Fredholm integro-differential equations, Numerical methods, Approximate solutions, LU matrix factorization, Fluid dynamics.
