ON THE CONVERGENCE OF THE MFS-MPS SCHEME FOR 1D POISSON'S EQUATION

被引：2

作者：

Chen, C. S. ^{[1
,2
]}

Huang, C. -S. ^{[3
]}

Lin, K. H. ^{[3
]}

机构：

[1] Taiyuan Univ Technol, Sch Math, Taiyuan, Peoples R China

[2] Univ So Mississippi, Dept Math, Hattiesburg, MS 39406 USA

[3] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 804, Taiwan

来源：

INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS | 2013年 / 10卷 / 02期

关键词：

Multiquadric collocation method; meshless method; error estimate; arbitrary precision computation; increasingly flat radial basis function; the method of fundamental solutions; the method of particular solutions; FUNDAMENTAL-SOLUTIONS; SCATTERED DATA; APPROXIMATION; INTERPOLATION;

D O I：

10.1142/S0219876213410065

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

The method of fundamental solutions (MFS) has been an effective meshless method for solving homogeneous partial differential equations. Coupled with radial basis functions (RBFs), the MFS has been extended to solve the inhomogeneous problems through the evaluation of the approximate particular solution and homogeneous solution. In this paper, we prove the the approximate solution of the above numerical process for solving 1D Poisson's equation converges in the sense of Lagrange interpolating polynomial using the result of Driscoll and Fornberg [2002].

引用

页数：13

共 16 条

[1] [Anonymous], LECT NOTES STAT
[2] Buhmann M.D., 2003, C MO AP C M, V12, P259, DOI 10.1017/CBO9780511543241
[3] Chen C.S., 2008, The Method of Fundamental Solutions-A Meshless Method, P75
[4] THE METHOD OF FUNDAMENTAL-SOLUTIONS FOR NONLINEAR THERMAL EXPLOSIONS
CHEN, CS
[J]. COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING, 1995, 11 (08): : 675 - 681
[5] On the equivalence of the Trefftz method and method of fundamental solutions for Laplace and biharmonic equations
Chen, J. T.
Wu, C. S.
Lee, Y. T.
Chen, K. H.
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2007, 53 (06) : 851 - 879
[6] Equivalence between the Trefftz method and the method of fundamental solution for the annular Green's function using the addition theorem and image concept
Chen, Jeng-Tzong
Lee, Ying-Te
Yu, Shang-Ru
Shieh, Shiang-Chih
[J]. ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2009, 33 (05) : 678 - 688
[7] Interpolation in the limit of increasingly flat radial basis functions
Driscoll, TA
Fornberg, B
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2002, 43 (3-5) : 413 - 422
[8] The method of fundamental solutions for elliptic boundary value problems
Fairweather, G
Karageorghis, A
[J]. ADVANCES IN COMPUTATIONAL MATHEMATICS, 1998, 9 (1-2) : 69 - 95
[9] Golberg M.A., 1998, Boundary Integral Methods, P103
[10] Improved multiquadric approximation for partial differential equations
Golberg, MA
Chen, CS
Karur, SR
[J]. ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 1996, 18 (01) : 9 - 17

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