Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 203, Issue 1, Pages 32-56Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cam.2006.03.009
Keywords
finite-difference rnethod; conservation; nonlinear wave equation; Boussinesq equation
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New conservative finite difference schemes for certain classes of nonlinear wave equations are proposed. The key tool there is discrete variational derivative, by which discrete conservation property is realized. A similar approach for the target equations was recently proposed by Furihata, but in this paper a different approach is explored, where the target equations are first transformed to the equivalent system representations which are more natural forms to see conservation properties. Applications for the nonlinear Klein-Gordon equation and the so-called good Boussinesq equation are presented. Numerical examples reveal the good performance of the new schemes. (c) 2006 Elsevier B.V. All rights reserved.
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