An Iterative Method for Solving Two Dimensional Nonlinear Volterra Integral Equations

Document Type : Research Paper

Author

Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran

Abstract

In this paper, a numerical iterative algorithm based on combination of the successive approximations method and the quadrature formula for solving two-dimensional nonlinear Volterra integral equations is proposed. This algorithm uses a trapezoidal quadrature rule for Lipschitzian functions applied at each iterative step. The convergence analysis and error estimate of the method are proved. Finally, two numerical examples are presented to show the accuracy of the proposed method.

Keywords

References

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Global Analysis and Discrete Mathematics
Volume 6, Issue 1
August 2021
Pages 41-57

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History

  • Receive Date: 22 November 2020
  • Revise Date: 14 January 2021
  • Accept Date: 09 February 2021

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