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Newton-Krylov generalized minimal residual algorithm in solving the nonlinear two-dimensional integral equations of the second kind on non-rectangular domains with an error estimate

    Authors

    • Hafez Yari 1
    • Mehdi Delkhosh 2

    1 Department of Computer Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran.

    2 Department of Mathematics and Computer Science, Bardaskan Branch, Islamic Azad University, Bardaskan, Iran.

,

Document Type : Regular paper

10.52547/CMCMA.1.2.35
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Abstract

In this paper, an applicable numerical approximation has been proposed for solving nonlinear two-dimensional integral equations (2DIEs) of the second kind on non-rectangular domains. Because directly applying the collocation methods on non-rectangular domains is difficult, in this work, at first, the integral equation is converted to an equal integral equation on a rectangular domain, then the solution is approximated by applying 2D Jacobi collocation method, the implementation of these instructions reduces the integral equation to a system of nonlinear algebraic equations, therefore, solving this system has an important role to approximate the solution. In this paper, Newton-Krylov generalized minimal residual (NK-GMRes) algorithm is used for solving the system of nonlinear algebraic equations. Furthermore, an error estimate for the presented method is investigated and several examples confirm the accuracy and efficiency of the proposed instructions.

Keywords

  • Non-rectangular domains
  • 2D integral equations
  • Jacobi polynomials
  • Collocation method
  • Newton-Krylov GMRes algorithm
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Computational Mathematics and Computer Modeling with Applications (CMCMA)
Volume 1, Issue 2 - Serial Number 2
December 2022
Pages 35-45
Files
  • XML
  • PDF 420.46 K
History
  • Receive Date: 31 October 2022
  • Revise Date: 08 December 2022
  • Accept Date: 29 December 2022
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How to cite
  • RIS
  • EndNote
  • Mendeley
  • BibTeX
  • APA
  • MLA
  • HARVARD
  • CHICAGO
  • VANCOUVER
Statistics
  • Article View: 122
  • PDF Download: 206

APA

Yari, H. and Delkhosh, M. (2022). Newton-Krylov generalized minimal residual algorithm in solving the nonlinear two-dimensional integral equations of the second kind on non-rectangular domains with an error estimate. Computational Mathematics and Computer Modeling with Applications (CMCMA), 1(2), 35-45. doi: 10.52547/CMCMA.1.2.35

MLA

Yari, H. , and Delkhosh, M. . "Newton-Krylov generalized minimal residual algorithm in solving the nonlinear two-dimensional integral equations of the second kind on non-rectangular domains with an error estimate", Computational Mathematics and Computer Modeling with Applications (CMCMA), 1, 2, 2022, 35-45. doi: 10.52547/CMCMA.1.2.35

HARVARD

Yari, H., Delkhosh, M. (2022). 'Newton-Krylov generalized minimal residual algorithm in solving the nonlinear two-dimensional integral equations of the second kind on non-rectangular domains with an error estimate', Computational Mathematics and Computer Modeling with Applications (CMCMA), 1(2), pp. 35-45. doi: 10.52547/CMCMA.1.2.35

CHICAGO

H. Yari and M. Delkhosh, "Newton-Krylov generalized minimal residual algorithm in solving the nonlinear two-dimensional integral equations of the second kind on non-rectangular domains with an error estimate," Computational Mathematics and Computer Modeling with Applications (CMCMA), 1 2 (2022): 35-45, doi: 10.52547/CMCMA.1.2.35

VANCOUVER

Yari, H., Delkhosh, M. Newton-Krylov generalized minimal residual algorithm in solving the nonlinear two-dimensional integral equations of the second kind on non-rectangular domains with an error estimate. Computational Mathematics and Computer Modeling with Applications (CMCMA), 2022; 1(2): 35-45. doi: 10.52547/CMCMA.1.2.35

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