Numerical simulation to the FitzHugh-Nagumo model with strong reaction
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The Fitzhugh-Nagumo model is a mathematical model derived from the simulation of propagating pulses in multicellular organisms. Since its creation, this model has drawn great attentions from academics and industry. To better understand the properties underlying this system, suitable numerical methods are needed to study it. In this thesis, numerical methods including the finite difference method, the finite element method, and the least-squares finite element method are applied to approximate its traveling wave solutions. In particular, since the FitzHugh-Nagumo model with strong reaction has a significant role in application, appropriate numerical scheme is designed to study it. Consistency and stability of the methods will been investigated. Numerical results are provided to illustrate the performances of the methods on the FitzHugh-Nagumo model under different cases.