JSIAM Letters
Online ISSN : 1883-0617
Print ISSN : 1883-0609
ISSN-L : 1883-0617
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A novel discrete variational derivative method using ``average-difference methods''
Daisuke FurihataShun SatoTakayasu Matsuo
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2016 Volume 8 Pages 81-84

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Abstract

We consider conservative numerical methods for a certain class of PDEs, for which standard conservative methods are not effective. There, the standard skew-symmetric difference operators indispensable for the discrete conservation law cause undesirable spatial oscillations. In this letter, to circumvent this difficulty, we propose a novel ``average-difference method,'' which is tougher against such oscillations. However, due to the lack of the apparent skew-symmetry, the proof of the discrete conservation law becomes nontrivial. In order to illustrate partially the superiority, we compare the standard and proposed methods for the linear Klein--Gordon equation.

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© 2016, The Japan Society for Industrial and Applied Mathematics
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