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KIAM Preprint № 1, Moscow, 2021
Authors: Bykovskaya E.N., Shapranov A.V., Mazhukin V.I.
Analysis of the error of approximation of two-layer difference schemes for the Korteweg de Vries equation
Abstract:
A family of weighted two-layer finite-difference schemes is presented. Using the example of the numerical solution of model problems on the propagation of a single soliton and the interaction of two solitons, the high quality of explicit-implicit schemes of the Crank-Nichols type with a weight parameter of 0.5 and a second order of approximation in the time and space variables is shown. Absolute stability with a low accuracy of the solution due to a large approximation error is characteristic of completely implicit two-layer difference schemes with a weight parameter of 1, first order in time and second in space. A family of explicitly implicit difference schemes is absolutely unstable if the explicitness parameter less than 0.5 prevails. Analysis of the structure of the approximation error, performed using the modified equation method, confirmed the results of numerical simulation.
Keywords:
two-layer finite-difference schemes, Korteweg-de Vries equation, Euler variables, soliton solutions
Publication language: russian,  pages: 17
Research direction:
Mathematical problems and theory of numerical methods
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About authors:
  • Bykovskaya Elena Nikolaevna,  orcid.org/0000-0002-3369-071XKIAM RAS
  • Shapranov Alexander Viktorovich,  orcid.org/0000-0001-8851-2286KIAM RAS
  • Mazhukin Vladimir Ivanovich,  orcid.org/0000-0001-5590-3731KIAM RAS