Shifted Jacobi collocation method for Volterra-Fredholm integral equation

Document Type : Research Paper

Author

Department of Mathematics, Faculty of Science, Helwan University, Egypt.

Abstract

In this paper, we compute the approximate numerical solution for the Volterra-Fredholm integral equation (VFIE) by using the shifted Jacobi collocation (SJC) method which depends on the operational matrices. Some properties of the shifted Jacobi polynomials are introduced. These properties allow us to transform the VolterraFredholm integral equation into a system of algebraic equations in a nice form with the expansion coefficients of the solution. Also, the convergence and error analysis are studied extensively. Finally, some examples which verify the efficiency of the given method are supplied and compared with other methods. 

Keywords

References

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Computational Methods for Differential Equations
Volume 10, Issue 2
April 2022
Pages 408-418

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History

  • Receive Date: 26 January 2020
  • Revise Date: 23 April 2021
  • Accept Date: 01 May 2021

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