On Some Problems of the Numerical Implementation of Nonlinear Systems on Example of KPI Equation
Faculty of Applied Mathematics and Control Processes, Saint-Petersburg State University,
2 Plekhanov Russian University of Economics, Stremyanny lane 36, 117997 Moscow, Russia
★ e-mail: firstname.lastname@example.org
Published online: 20 January 2020
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.
© The Authors, published by EDP Sciences, 2020
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