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Numerical solution to a linearized KdV equation on unbounded domain
Author(s) -
Zheng Chunxiong,
Wen Xin,
Han Houde
Publication year - 2008
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20267
Subject(s) - mathematics , korteweg–de vries equation , boundary value problem , partial differential equation , boundary (topology) , domain (mathematical analysis) , mathematical analysis , galerkin method , scheme (mathematics) , dual (grammatical number) , partial derivative , finite element method , physics , quantum mechanics , nonlinear system , thermodynamics , art , literature
Exact absorbing boundary conditions for a linearized KdV equation are derived in this paper. Applying these boundary conditions at artificial boundary points yields an initial‐boundary value problem defined only on a finite interval. A dual‐Petrov‐Galerkin scheme is proposed for numerical approximation. Fast evaluation method is developed to deal with convolutions involved in the exact absorbing boundary conditions. In the end, some numerical tests are presented to demonstrate the effectiveness and efficiency of the proposed method.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008