A discrete Fourier method for numerical solution of strongly coupled mixed parabolic systems
The article deals with the system of strongly coupled parabolic partial differential equations arising in diffusion processes, microwave engineering or geomechanics. The proposed numerical scheme is based on the spatio-temporal discretisation by the Crank-Nicolson method. The authors suggest to treat the numerical scheme by means of the discrete Fourier method and a decomposition of discrete spatial and time dependence. This approach leads to a possibility of proving stability of the derived scheme. The results are related to those of \textit{L. Jodar} and \textit{M. C. Casaban} [Math. Comput. Modelling 34, 283--297 (2001; Zbl 0994.65096)].
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