A new approach to solve Fredholm and Volterra integral equations
Subject Areas : Case Studies and Best Practices
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Keywords: : Fourier series, Linear programming, Infinite dimensional moment problem, Fredholm and Volterra integral equations,
Abstract :
In recent years, integral equations have attracted the attention of many researchers. These equations are used in solving differential equations with partial derivatives and ordinary differential equations. A special type of integral equations are Volterra integral equations. Volterra integral equations are used in demograph-y as Lotka's integral equation, the study of viscoelastic materials, in actuarial science through the renewal equation, and in fluid mechanics to describe the flow behavior near finite-sized boundaries. In this paper, a new approach to numerical solution of Volterra integral equations is presented. In this paper, a new approach to numerical solution of Volterra integral equations is presented. In this method, The Volterra integral equations are first converted to an infinite dimension moment problem. Then, the infinite dimension moment problem is converted to a finite dimension moment problem in an approximate way, so that the resulting error can be ignored. The finite dimensional moment problem is transformed to a linear programming problem, and finally, by solving this problem, the solution of the integral equations is obtained. The solution of the linear programming problem can be easily obtained using various softwares such as MATLAB. Using two examples, the performance of the proposed algorithm has been analysed. The simulations show that the proposed method has an acceptable performance.
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