Fredholm and Volterra integral equations appear for a number of branches of engineering sciences such as acoustic study, optics theory, laser, potential theory, and radioactive radiation theory, study of heart disease curves, fluid mechanics, and communication and so on. Since in most cases it is not possible to find an analytical solution of the problem, so it is necessary to find numerical solution of under consideration problem. In this research project, for the first time, the idea of a modified Simpson’s quadrature method was proposed and it was used to obtain numerical solution of the second type of Volterra linear integral equations. Using this method, the second type Volterra linear integral equations will be transformed into a set of algebraic equations. Then we show that the approximate solution of the second type Volterra linear integral equations are highly accurate. Furthermore, error approximation of second type Volterra linear integral equations for modified Simpson’s quadrature method is O(h^6). In the continuation of this research project, orthogonal triangular functions are introduced and it is used to numerically solve the equations of the second type of linear Volterra integral equations. By using these functions, the second type of linear Volterra integral equations will be converted into a system of algebraic equations. To show the efficiency of numerical methods of this research project, we have used numerical algorithms on several examples by comparing the exact solutions.
