Exponential spline for the numerical solutions of linear Fredholm integro-differential equations

Abstract

Abstract In this paper, we introduce a new scheme based on the exponential spline function for solving linear second-order Fredholm integro-differential equations. Our approach consists of reducing the problem to a set of linear equations. We prove the convergence analysis of the method applied to the solution of integro-differential equations. The method is described and illustrated with numerical examples. The results reveal that the method is accurate and easy to apply. Moreover, results are compared with the method in (J. Comput. Appl. Math. 290:633–640, 2015).

Keywords

• Exponential spline
• Boundary conditions
• Integro-differential equation
• Diagonally-dominant matrix
• Convergence