Abstract
A numerical verification, method of steady state solutions for a system of reaction-diffusion equations is described. Using a decoupling technique, the system is reduced to a single nonlinear equation and a computer-assisted method for second-order elliptic boundary value problems based on the infinite dimensional fixed-point theorem can be applied. Some numerical examples confirm the effectiveness of the method.
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Watanabe, Y. A numerical verification method for two-coupled elliptic partial differential equations. Japan J. Indust. Appl. Math. 26, 233–247 (2009). https://doi.org/10.1007/BF03186533
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DOI: https://doi.org/10.1007/BF03186533