| Autor: |
MAZHUKIN, V. I., SHAPRANOV, A. V., BYKOVSKAYA, E. N. |
| Zdroj: |
Mathematica Montisnigri; 2020, Vol. 49, p57-69, 13p |
| Abstrakt: |
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 the parameter σ = 0.5 and the order of approximation O(Δt² + Δx²) is shown. Completely implicit two-layer difference schemes with the parameter σ = 1 and O (Δt + Δx²) are characterized by absolute stability with a low solution accuracy due to a high approximation error. The family of explicitly implicit difference schemes is absolutely unstable if the explicitness parameter σ <0.5 prevails. Analysis of the structure of the approximation error, performed using the modified equation method, confirmed the results of numerical simulation. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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