On Some Problems of the Numerical Implementation of Nonlinear Systems on Example of KPI Equation
| Autor: | Vladimir V. Mareev, Alexander V. Bogdanov |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Convection
Computer simulation 010308 nuclear & particles physics Physics QC1-999 Finite difference method 020206 networking & telecommunications 02 engineering and technology Wave equation 01 natural sciences Nonlinear system 0103 physical sciences 0202 electrical engineering electronic engineering information engineering Applied mathematics Trimming Boundary value problem Representation (mathematics) |
| Zdroj: | EPJ Web of Conferences, Vol 226, p 01003 (2020) |
| ISSN: | 2100-014X |
| DOI: | 10.1051/epjconf/202022601003 |
| Popis: | Analytical and numerical peculiarities of solving nonlinear problems are considered on examples of wave equations like KdVB and Kadomtsev-Petviashvili-I equation (KPI). KPI is represented in integro-differential form. Main attention is paid to the problem of asymptotical behavior of solution and appearance of nonphysical artefacts. The numerical solution is carried out by the finite difference method. For a correct representation of the boundary condition along the y axis in numerical simulation a method is proposed for introducing small artificial convection into the original equation in the indicated direction. Along with the introduction of artificial convection, the procedure of trimming of the integral on the bands adjacent to the upper and lower boundaries of the calculated region is used. The results obtained by numerical testing, showed sufficient accuracy and validity of this procedure. |
| Databáze: | OpenAIRE |
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