A Fibonacci collocation method for solving a class of Fredholm–Volterra integral equations in two-dimensional spaces

Abstract

In this paper, we present a numerical method for solving two-dimensional Fredholm–Volterra integral equations (F-VIE). The method reduces the solution of these integral equations to the solution of a linear system of algebraic equations. The existence and uniqueness of the solution and error analysis of proposed method are discussed. The method is computationally very simple and attractive. Finally, numerical examples illustrate the efficiency and accuracy of the method.

Keywords

• Two-dimensional Fredholm–Volterra integral equations
• The Fibonacci polynomials
• Collocation method