A New Numerical Technique for Solving Volterra Integral Equations Using Chebyshev Spectral Method

Abstract

In this work, we propose a new method for solving Volterra integral equations. The technique is based on the Chebyshev spectral collocation method. The application of the proposed method leads Volterra integral equation to a system of algebraic equations that are easy to solve. Some examples are presented and compared with some methods in the literature to illustrate the ability of this technique. The results demonstrate that the new method is more efficient, convergent, and accurate to the exact solution.

New Solution Method for Solving Volterra Integral Equation Using Bernstein Polynomials

“…Yu-Ming Chu and et al in [10] are offers Numerical investigation of Volterra integral Equations of second type using most effective Homotopy Asymptotic technique. Khidir in [11] is present a brand new Numerical approach for solving Volterra integral Equations using Chebyshev Spectral technique. Inside the proposed approach, we introduce a new integral transformation that is the substitute of an integral term in the Volterra integral equation with the aid of Bernstein Polynomials.…”

The Spectral Adomian Decomposition Method for the Solution of MHD Jeffery–Hamel Problem

“…Te proposed method herein is referred to as the spectral Adomian decomposition method (SADM). Te new technique was frst studied by Yassir and Khidir [25], and they applied the new modifcation on the problem of boundary layer convective heat transfer over plate, and they showed that the new modifcation is more efcient than the standard ADM. Tis technique is based on the blending of the Chebyshev pseudospectral methods (see [26][27][28][29][30][31][32][33][34][35]) and the Adomian decomposition method. In this method, they expressed the linear operator in terms of the Chebyshev spectral diferentiation matrix.…”

Study on Determining the Blood Glucose Concentration During an Intravenous Injection Using Volterra Integral Equations

“…Recently, Chauhan and Aggarwal [10] used Laplace transform for solving linear Volterra integral equation of second kind, Aggarwal et. all [11] applied Shehu transform for handling Volterra integral equations of first kind, Barycentric -Maclaurin interpolation method has been applied by [12] for solving Volterra integral equations of the second kind, Khidir [13,14] suggest a highly accurate technique for solving Volterra integral equations based on the blending of the Chebyshev pseudo methods. Chebyshev spectral collocation methods have been applied successfully in different fields of sciences because of their ability to give very high accurate solutions of single or system of boundary value problems, this is because Chebyshev spectral methods are defined everywhere in the computational domain [15][16][17][18][19][20][21][22][23][24].…”