# Numerical Approximations of Fredholm-Volterra Integral Equation of 2nd kind using Galerkin and Collocation Methods

## Keywords:

Fredholm-Volterra integral equations, Galerkin method, collocation method, polynomials## Abstract

Galerkin and collocation approximation techniques are very effective and popular among researchers for numerical approximations of different types of differential, integral and integro-differential equations. Both methods approximate the solution by a finite sum of some known polynomials. In recent years, researchers around the world have been used different combinations of polynomials and collocation points in Galerkin and collocation methods for numerical approximations of different types of integral equations. Also, collocation method have been used more frequently compared to the Galerkin method. In this research, five different polynomials in

Galerkin method and five different combinations of polynomials and collocation points in collocation method have been used for numerical approximations of linear FVIE of 2nd kind.It is found that the performances of different polynomials and collocation points in both these methods are consistent.

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*Suan Sunandha Science and Technology Journal*,

*7*(2), 15–22. Retrieved from https://li02.tci-thaijo.org/index.php/ssstj/article/view/368