A semi-lagrangian numerical method for geometric optics type problems |
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| Authors: | J-D Benamou |
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| Institution: | (1) Department of Mathematics, University of Auckland, Private Bag 92019, 1030 Auckland, New Zealand;(2) Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, England |
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| Abstract: | Linear multistep methods (LMMs) are written as irreducible general linear methods (GLMs). A-stable LMMs are shown to be algebraically
stable GLMs for strictly positive definite G-matrices. Optimal order error bounds, independent of stiffness, are derived for A-stable methods, without considering one-leg
methods (OLMs). As a GLM, the OLM is shown to be the transpose of the LMM. For A-stable methods, the LMM G-matrix is the inverse of the OLM G-matrix. Examples of G-symplectic LMMs are given.
AMS subject classification (2000) 65L20 |
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| Keywords: | linear multistep methods general linear methods G-stability |
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