Shifted Legendre method with residual error estimation for delay linear Fredholm integro-differential equations

Abstract

In this paper, we suggest a matrix method for obtaining the approximate solutions of the delay linear Fredholm integro-differential equations with constant coefficients using the shifted Legendre polynomials. The problem is considered with mixed conditions. Using the required matrix operations, the delay linear Fredholm integro-differential equation is transformed into a matrix equation. Additionally, error analysis for the method is presented using the residual function. Illustrative examples are given to demonstrate the efficiency of the method. The results obtained in this study are compared with the known results.

Keywords

• Delay Fredholm integro-differential equations
• Numerical solution
• Matrix method
• Shifted Legendre polynomials