Geodesic
A frequency decomposition waveform relaxation algorithm for semilinear evolution equations
Electronic transactions on numerical analysis, Tome 17 (2004), pp. 181-194.

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Summary: Semilinear evolution equations arise in many applications ranging from mathematical biology to chemical reactions (e.g., combustion). The significant difficulty in these equations is the nonlinearity, which combined with the discretized diffusion operator leads to large systems of nonlinear equations. To solve these equations, Newton's method or a variant thereof is often used, and to achieve convergence can require individual fine tuning for each case. This can be especially difficult if nothing is known about the solution behavior. In addition, one observes in many cases that not all frequency components are equally important for the solution; the frequency interaction is determined by the nonlinearity. It is therefore of interest to work in frequency space when analyzing the unknown behavior of such problems numerically.
Classification : 65M70, 65M55, 65H10
Keywords: waveform relaxation, frequency decomposition, sequential spectral method, iterative approximation of evolution problems 
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     author = {Gander, Martin J.},
     title = {A frequency decomposition waveform relaxation algorithm for semilinear evolution equations},
     journal = {Electronic transactions on numerical analysis},
     pages = {181--194},
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     volume = {17},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2004__17__a3/}
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Gander, Martin J. A frequency decomposition waveform relaxation algorithm for semilinear evolution equations. Electronic transactions on numerical analysis, Tome 17 (2004), pp. 181-194. http://geodesic.mathdoc.fr/item/ETNA_2004__17__a3/