Solving linear Volterra-Fredholm integral equation of the second type using linear programming method

Abstract EN

In this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases).

The new technique depends on approximating the solution to a polynomial of degree (m-1) and ther7efore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE.

Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE.

Also, a comparison between those methods is produced.

Finally, for more explanation, an algorithm is proposed and applied for testing examples to illustrate the effectiveness of the new technique.