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- W2000569280 abstract "In this work, we present a finite-difference scheme that preserves the non-negativity and the boundedness of some solutions of a FitzHugh–Nagumo equation. The method is explicit, and it approximates the solutions of the nonlinear, parabolic partial differential equation under study with a consistency of order 𝒪 (Δ t+(Δ x)2) in the Dirichlet regime investigated. We give sufficient conditions in terms of the computational and the model parameters, in order to guarantee the non-negativity and the boundedness of the approximations. We also provide analyses of consistency, linear stability and convergence of the method. Our simulations establish that the properties of non-negativity and boundedness are actually preserved by the scheme when the proposed constraints are satisfied. Finally, a comparison against some second-order accurate methods reveals that our technique is easier to implement computationally, and it is better at preserving the properties of non-negativity and boundedness of the solutions of the FitzHugh–Nagumo equation under study." @default.
- W2000569280 created "2016-06-24" @default.
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- W2000569280 date "2011-10-01" @default.
- W2000569280 modified "2023-10-17" @default.
- W2000569280 title "A finite-difference scheme to approximate non-negative and bounded solutions of a FitzHugh–Nagumo equation" @default.
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- W2000569280 doi "https://doi.org/10.1080/00207160.2011.579964" @default.
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