Nonlinear Instability in Dissipative Finite Difference Schemes
Copyright policy )Nonlinear Instability in Dissipative Finite Difference Schemes
A unified analysis of reaction-diffusion equations and their finite difference representations is presented. Continuous and discrete problems are studied from the perspective of bifurcation theory. The numerical instability is shown to be associated with the bifurcation of periodic orbits in discrete systems. The new work presented in this paper is an analytical description of the nonlinear interaction of a high wavenumber mode, which is a product of the discretization, and a low wavenumber mode presented in the governing differential equation.
- California Institute of Technology United States
finite difference, numerical instability, Stability and convergence of numerical methods for boundary value problems involving PDEs, 510, periodic orbits, reaction-diffusion equations, Reaction-diffusion equations, dissipation and nonlinearity, bifurcation, discrete systems, bifurcation and instability, low wavenumber mode, high wavenumber mode, continuous and discrete problems
finite difference, numerical instability, Stability and convergence of numerical methods for boundary value problems involving PDEs, 510, periodic orbits, reaction-diffusion equations, Reaction-diffusion equations, dissipation and nonlinearity, bifurcation, discrete systems, bifurcation and instability, low wavenumber mode, high wavenumber mode, continuous and discrete problems
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