On convergence of the method of fundamental solutions for solving the Dirichlet problem of Poisson's equation

Advances in Computational Mathematics

Volumn 23, Issue 3, 2005, Pages 265-277

  Li, Xin ^a  

^a UNIVERSITY OF NEVADA   (United States)

Author keywords

Method of fundamental solutions; Poisson's equation

Indexed keywords

EID: 33646719648     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10444-004-1782-z     Document Type: Article

References (24)

1. M.A. Aleksidze, On approximate solutions of a certain mixed boundary value problem in the theory of harmonic functions, Diff. Equations 2 (1966) 515-518.
2. C.S. Chen, The method of fundamental solutions for nonlinear thermal explosion, Comm. Numer. Methods Engrg. 11 (1995) 675-681.
3. R.S.C. Cheng, Delta-trigonometric and spline methods using the single-layer potential representation, Ph.D. dissertation, University of Maryland (1987).
4. G. Fairweather and A. Karageorghis, The method of fundamental solutions for elliptic boundary value problems, Adv. Comput. Math. 9 (1998) 69-95.
5. W. Freeden and H. Kersten, A constructive approximation theorem for the oblique derivative problem in potential theory, Math. Methods Appl. Sci. 3 (1981) 104-114.
6. M. A. Golberg, The method of fundamental solutions for Poisson's equation, Engrg. Anal. Boundary Elem. 16 (1995) 205-213.
7. M.A. Golberg and C.S. Chen, Discrete Projection Methods for Integral Equations (Computational Mechanics Publications, Southampton, 1996).
8. M.A. Golberg and C.S. Chen, The method of fundamental solutions for potential Helmholtz and diffusion problems, in: Boundary Integral Methods - Numerical and Mathematical Aspects, ed. M.A. Golberg (Computational Mechanics Publications, Southampton, 1998) pp. 103-176.
9. I.S. Gradshteyn and I.M. Ryzhik, Tables of Integrals Series and Products (Academic Press, New York, 1965).
10. A. Karageorghis and G. Fairweather, The method of fundamental solutions for the solution of nonlinear plane potential problems, IMA J. Numer. Anal. 9 (1989) 231-242.
11. M. Katsurada, A mathematical study of the charge simulation method II, J. Fac. Sci. Univ. Tokyo, Sect. 1A Math. 36 (1989) 135-162.
12. M. Katsurada, Asymptotic error analysis of the charge simulation method in a Jordan region with an analytic boundary, J. Fac. Sci. Univ. Tokyo, Sect. 1A Math. 37 (1990) 635-657.
13. M. Katsurada, Charge simulation method using exterior mapping functions, Japan J. Industr. Appl. Math. 11 (1994) 47-61.
14. M. Katsurada and H. Okamoto, A mathematical study of the charge simulation method I, J. Fac. Sci. Univ. Tokyo, Sect. 1A Math. 35 (1988) 507-518.
15. M. Katsurada and H. Okamoto, The collocation points of the fundamental solution method for the potential problem, Comput. Math. Appl. 31 (1996) 123-137.
16. T. Kitagawa, On the numerical stability of the method of fundamental solution applied to the Dirichlet problem, Japan J. Appl. Math. 5 (1988) 123-133.
17. V.D. Kupradze, A method for the approximate solution of limiting problems in mathematical physics, Comput. Math. Math. Phys. 4 (1964) 199-205.
18. V.D. Kupradze and M.A. Aleksidze, The method of functional equations for the approximate solution of certain boundary value problems, Comput. Math. Math. Phys. 4 (1964) 82-126.
19. P.K. Kythe, Fundamental Solutions for Differential Operators and Applications (Birkhäuer, Boston, 1996).
20. X. Li and M.A. Golberg, On the convergence of the dual reciprocity method for Poisson's equation, in: Transformation of Domain Effects to the Boundary, ed. Y.F. Rashed (WIT Press, Southampton/Boston, 2003) pp. 227-251.
21. X. Li, C.H. Ho and C.S. Chen, Computational Test of Approximation of Functions and their derivatives by radial basis functions, Neural Parallel Sci. Comput. 10 (2002) 25-46.
22. X. Li and C.A. Micchelli, Approximation by radial bases and neural networks, Numer. Algorithms 25 (2000) 241-262.
23. C. Miranda, Partial Differentail Equations of Elliptic Type (Springer, New York, 1970).
24. Y.S. Smyrlis and A. Karageorghis, Some aspects of the method of fundamental solutions for certain harmonic problems, J. Sci. Comput. 16(3) (2001) 341-371.