Abstract
An efficient and accurate numerical scheme is proposed, analyzed and implemented for the Kawahara and modified Kawahara equations which model many physical phenomena such as gravity-capillary waves and magneto-sound propagation in plasmas. The scheme consists of dual-Petrov-Galerkin method in space and Crank-Nicholson-leap-frog in time such that at each time step only a sparse banded linear system needs to be solved. Theoretical analysis and numerical results are presented to show that the proposed numerical is extremely accurate and efficient for Kawahara type equations and other fifth-order nonlinear equations.
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This work is partially supported by the National Science Council of the Republic of China under the grant NSC 94-2115-M-126-004 and 95-2115-M-126-003.
This work is partially supported by NSF grant DMS-0610646.
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Yuan, JM., Shen, J. & Wu, J. A Dual-Petrov-Galerkin Method for the Kawahara-Type Equations. J Sci Comput 34, 48–63 (2008). https://doi.org/10.1007/s10915-007-9158-4
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DOI: https://doi.org/10.1007/s10915-007-9158-4