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Author

Lee, Chang Hyeong
Stochastic Analysis & Simulation(SAS) Lab
Research Interests
  • Stochastic analysis/computation, epidemic modeling, biological system simulation

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A NUMERICAL METHOD FOR SPATIALLY NON-DECAYING CONSERVATION LAWS ON UNBOUNDED DOMAINS

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Title
A NUMERICAL METHOD FOR SPATIALLY NON-DECAYING CONSERVATION LAWS ON UNBOUNDED DOMAINS
Author
Lee, Chang HyeongKim, Pilwon
Keywords
Conservation Laws; Geometric Integraion; Exact Solutions; Unbounded Domain
Issue Date
201309
Publisher
AZERBAIJAN NATIONAL ACAD SCI
Citation
APPLIED AND COMPUTATIONAL MATHEMATICS, v.12, no.3, pp.365 - 372
Abstract
We discuss a numerical method for scalar conservation laws on multi dimensional unbounded domains. Since numerical approximations are made on a finite region, it is generally challenging to handle a solution that never diminishes on the open domain The presented scheme does not require an assumption that a solution decays to zero at infinity, which is different from conventional methods based on artificial boundary conditions. The algorithm is introduced from fixed-point iteration on implicit solutions that conservation laws possess. We can successfully reproduce shock formation occurring over open domain in nonlinear conservation laws. Several numerical results, including one and two dimensional Burgers' equations, are illustrated and compared to those from a conventional shock-handling method such as the WENO scheme.
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ISSN
1683-3511
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