Abstract
The stability theory of finite difference approximations to linear partial differential equations is largely based on that for the special case in which the coefficients of the equations are constant and the boundary conditions are periodic. In that case one can employ a Fourier analysis to reduce the problem to the study of families of matrices G, the amplification matrices (see Lax and Richtmyer [6]). If vv is the Fourier transform of the solution vector at the vth time step, then vv = Gvvo and the stability of the difference scheme is equivalent to the uniform boundedness of Gv for vAt ^ 1, where At is the time step. A rather more convenient and equivalent form of this condition is that there should exist a constant a > 0 such that the matrices A = eaAtG satisfy
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