# A numerical verification method for two-coupled elliptic partial differential equations

@article{Watanabe2009ANV, title={A numerical verification method for two-coupled elliptic partial differential equations}, author={Yoshitaka Watanabe}, journal={Japan Journal of Industrial and Applied Mathematics}, year={2009}, volume={26}, pages={233-247} }

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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