Dynamical knot and shape parameter setting for simulating shock wave by using multi-quadric quasi-interpolation |
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| Affiliation: | 1. Jiangsu Key Laboratory of Green Synthetic Chemistry for Functional Materials, Jiangsu Normal University, Xuzhou 221116, P.R.China;2. School of Chemistry and Chemical Engineering, Jiangsu Normal University, Xuzhou 221116, P.R.China;1. Department of Applied Mathematics, Guangdong University of Finance, Guangzhou 510521, China;2. Guangzhou University Sontan College, Guangzhou 511370, China;3. School of Mathematics Science, South China Normal University, Guangzhou 510631, China;1. Key Laboratory of Neurology of Hebei Province, The Second Hospital of Hebei Medical University, Shijiazhuang, Hebei 050000, China;2. Department of Pediatrics, The Second Hospital of Hebei Medical University, Shijiazhuang, Hebei 050000, China;3. Department of Acupuncture and Moxibustion, The Traditional Chinese Medicine Hospital of Shijiazhuang, Hebei 050000, China |
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| Abstract: | In order to solve non-linear wave equation numerically, three features are demonstrated in this paper. First we move the knots dynamically to keep the data denser near the shocks than elsewhere. Second we set the shape parameters of the multi-quadric dynamically to get an efficient simulation of the shock wave. Finally we use quasi-interpolation served as viscosity step by step respected to the discrete time level. Theoretical discussion for the shape preserving and the variation diminishing property (the base point of the stability of the scheme) is showed in the paper too. Numerical example shows that the method works very well. |
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