Abstract
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.
Highlights
Integral equations occur naturally in many optimal solution of the latest problem as an fields of mechanics and mathematical physics
Skandari et al in 2011 proposed a new used the linear programming method to find approach for a class of optimal control problems to numerical solution of Volterra integral equations of solve Volterra integral equations which is based on the 2nd kind (2)
This paper presents a method of finding the solution of LVFIE of the 2nd kind using the LPP
Summary
Integral equations occur naturally in many optimal solution of the latest problem as an fields of mechanics and mathematical physics. From the last few years, there has been nonlinear Fredholm integral equations of the second interest to use the linear and nonlinear programming kind with the continuous kernel by converting the methods to find a numerical or approximate integral equation problem into an optimization solution for integral equations. Skandari et al in 2011 proposed a new used the linear programming method to find approach for a class of optimal control problems to numerical solution of Volterra integral equations of solve Volterra integral equations which is based on the 2nd kind (2). Khan et al in 2017 provided a numerical technique for obtaining approximate solution of mixed Volterra-Fredholm integral equations of 2nd kind based on the Bernstein’s approximation (17).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
