非線型偏微分方程式の安定なghost差分解の挙動解析

概要

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In this paper we want to analyze the characteristic behavior in a numerical solution of a nonlinear partial differential equation by utilizing the nonlinear dynamics approach such as a bifurcation diagram and the Lyapunov Exponent. To investigate the typical feature of spurious asymptotes(periodic points, limit cycles, tori and chaotic motions), and to discuss the speed of convergence to the steady-state solution could contribute new suggestions in the interpretation of numerical results. Some kinds of space discretization formulas such as a central difference, an upwind difference and so on, and the Euler forward difference scheme in time are applied to the one-dimensional Burgers' equation. Furthermore, we have a discussion about the first bifurcation point where the ghost solution appeares by applying the linear stability analysis.
日本応用数理学会の論文
1993-12-15