Comparison of Numerical Methods for Solutions of Linear Fredholm Integral Equation of the Second Kind

Abstract

The purpose of this study is to compare the efficiency of three methods; Trapezoidal rule method, Gauss-Nystrom method, and Hermite series Method for the solution of Linear Fredholm Integral Equation of the Second Kind. The numerical methods are involved in partition of grids and weight function for apporoximation of solutions and simplified to be a system of linear equation. The numerical solutions are illustrated and compared by Absolute Error measurement as errror analysis. Also,  one example is discussed and solved by three methods and the results are compared. The findings showed that Gauss-Nystrom method was more efficient than Trapezoidal rule and Hermite series method, which was based on minimum absolute error.