Solving Linear Volterra – Fredholm Integral Equation of the Second Type Using Linear Programming Method

Baghdad Science Journal

Muna Mansoor Mustafaf¹ 

[1] Department of Mathematics, College of Science for Women, University of Baghdad;

关键词: Linear Volterra-Fredholm integral equation of the 2nd kind (LVFIE), Linear programming problem (LPP), Quadrature methods.;   

DOI  :  10.21123/bsj.2020.17.1(Suppl.).0342

来源: DOAJ

【 摘 要 】

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  and therefore 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.

【 授权许可】

Unknown