Solving Robin condition using a method based on integral equation
*Mohsen AghaeiboorkheiliCorresponding authormohsen.aghaeiboorkheili@pnguot.ac.pgDepartment of Mathematics and Computer Science University of TechnologyLae, 411, Papua New GuineaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 15 Jun 2022
- Accepted:
- 16 Nov 2022
- Published Online:
- 29 Dec 2023
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-1636
- Pages:
- 1777–1785
Abstract
Keywords
Subject Classifications
References
[1] M. Jahanshahi, “Reduction of the Neumann, Poincare and Robin-Zaremba boundary value problems for Laplace equation to the Dirichlet boundary value problem,” Appl. Comput. Math., vol. 6, no. 1, pp. 51–57 (2007).
[2] S. Shiralashetti, M. Kantli, A. Deshi, and P. Mutalik Desai, “A modified wavelet multigrid method for the numerical solution of boundary value problems,” Journal of Information and Optimization Sciences, vol. 38, no. 1, pp. 151-172 (2017).
[3] L. Yong, “Richardson iteration for linear equations and application in two-point boundary value problem,” Journal of Interdisciplinary Mathematics, vol. 21, no. 1, pp. 231-242 (2018).
[4] P. Henrici, Applied and computational complex analysis. Vol. 3. Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1986. Discrete Fourier analysis—Cauchy integrals—construction of conformal maps—univalent functions, A Wiley-Interscience Publication.
[5] F. D. Gakhov, Boundary value problems. Dover Publications, Inc., New York, 1990. Translated from the Russian, Reprint of the 1966 translation.
[6] S. G. Mikhlin, Integral equations and their applications to certain problems in mechanics, mathematical physics and technology. Pergamon Press, New York-London-Paris-Los Angeles, 1957. Translated from the Russian by A. H. Armstrong.
[7] N. I. Muskhelishvili, Singular integral equations. Noordhoff International Publishing, Leyden, 1977. Boundary problems of function theory and their application to mathematical physics, Revised translation from the Russian, edited by J. R. M. Radok, Reprinted of the 1958 edition.
[8] R. Wegmann, A. H. M. Murid, and M. M. S. Nasser, “The Riemann-Hilbert problem and the generalized Neumann kernel,” J. Comput. Appl. Math., vol. 182, no. 2, pp. 388-415 (2005).
[9] M. Aghaeiboorkheili and A. Mohamed, “Applications of mechanical engineering mathematics: Solving neumann problem with discontinuous coefficients,” Journal of Interdisciplinary Mathematics, vol. 24, no. 5, pp. 1429-1439 (2021).
[10] M. M. S. Nasser, A. H. M. Murid, M. Ismail, and E. M. A. Alejaily, “Boundary integral equations with the generalized Neumann kernel for Laplace’s equation in multiply connected regions,” Appl. Math. Comput., vol. 217, no. 9, pp. 4710-4727 (2011).
[11] M. M. S. Nasser, A. H. M. Murid, and Z. Zamzamir, “A boundary integral method for the Riemann-Hilbert problem in domains with corners,” Complex Var. Elliptic Equ., vol. 53, no. 11, pp. 989-1008 (2008).
[12] K. E. Atkinson, The numerical solution of integral equations of the second kind, vol. 4 of Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, Cambridge, 1997.
