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Some comments on the ill-conditioning of the method of fundamental solutions. (English) Zbl 1187.65136
Summary: We consider the accuracy and stability of implementing the method of fundamental solutions. In contrast to the results shown by P. A. Ramachandran, Commun. Numer. Methods Eng. 18, No. 11, 789–801 (2002; Zbl 1016.65095)], we find that Gaussian elimination can be used reliably to solve the MFS equations and the use of the singular value decomposition shows no improvement over Gaussian elimination provided that the boundary condition is non-noisy. However, for noisy boundary conditions, there is evidence that the singular value decomposition with truncation is more accurate than Gaussian elimination.

65N80 Fundamental solutions, Green’s function methods, etc. for boundary value problems involving PDEs
65N20 Numerical methods for ill-posed problems for boundary value problems involving PDEs
Full Text: DOI
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