Numerical Solution of Second Kind Volterra and Fredholm Integral Equations Based on a Direct Method Via Triangular Functions

Subject Areas : International Journal of Industrial Mathematics

S. Hatamzadeh-Varmazyar ¹ (Department of Electrical Engineering, Islamshahr Branch, Islamic Azad University, Tehran, Iran.)
Z. Masouri ² (Department of Electrical Engineering, Islamshahr Branch, Islamic Azad University, Tehran, Iran.)

Received: 2017-04-27 Accepted : 2017-10-22 Published : 2019-04-01

Keywords: Approximate solution, Vector forms, Triangular functions, Integral equations of the second kind, Direct method,

Abstract :

A numerical method for solving linear integral equations of the second kind is formulated. Based on a special representation of vector forms of triangular functions and the related operational matrix of integration, the integral equation reduces to a linear system of algebraic equations. Generation of this system needs no integration, so all calculations can easily be implemented. Numerical results for some examples show that the method has a good accuracy.