Modified hierarchy basis for solving singular boundary value problems |
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Authors: | Song-Tao Liu |
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Institution: | Department of Mathematics, Syracuse University, Syracuse, NY, USA |
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Abstract: | In this paper, we develop an efficient preconditioning method on the basis of the modified hierarchy basis for solving the singular boundary value problem by the Galerkin method. After applying the preconditioning method, we show that the condition number of the linear system arising from the Galerkin method is uniformly bounded. In particular, the condition number of the preconditioned system will be bounded by 2 for the case q(x)=0 (see Eq. (1) in the paper). Numerical results are presented to confirm our theoretical results. |
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Keywords: | Modified hierarchy basis Preconditioning Stability Singular boundary value problem |
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