A nonstiff Euler discretization of the complex Ginzburg-Landau equation in one space dimension

作者：Takac P^*; Jungel A

来源：SIAM Journal on Numerical Analysis, 2000, 38(1): 292-328.

• complex Ginzburg Landau equation
• finite Fourier series approximation
• temporal Euler discretization

A nonstiff discretization method is applied to the complex Ginzburg Landau (CGL) equation with periodic boundary conditions,
partial derivative(t)u = (1 + i nu)partial derivative(xx)(2)u+ Ru - (1 + i mu)\u\(2)u;
u(x + 2 pi, t) = u(x, t) for -infinity < x < infinity, t greater than or equal to 0.
This parabolic equation is discretized first in space by a truncated Fourier series ( that is, a nite Fourier sum) and then in time by an explicit Euler method. The exponential decay of Fourier modes in both, the original CGL equation, and the resulting equation for the truncated Fourier series (independently from the number of Fourier modes in the truncation) is used in an essential way to prove the nonstiffness. Also dissipativity of the discretized equation is established and numerical results are discussed.

• 出版日期2000-6-23