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Simple numerical method to study traveling‐wave solutions of a diffusive problem with nonlinear advection and reaction
Author(s) -
MaciasDiaz Jorge,
Villa J.
Publication year - 2013
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21772
Subject(s) - mathematics , monotone polygon , simple (philosophy) , nonlinear system , advection , bounded function , partial differential equation , consistency (knowledge bases) , finite difference , fisher equation , mathematical analysis , space (punctuation) , finite difference method , computer science , geometry , philosophy , physics , epistemology , real interest rate , quantum mechanics , monetary economics , economics , thermodynamics , interest rate , operating system
In this manuscript, we propose a simple, two‐step, finite‐difference scheme to approximate the solutions of an advective Fisher's equation. The method proposed is nonlinear, explicit and, in the linear regime, it approximates the solutions of the equation of interest with a consistency of first order in time and second order in space. We prove that the technique is capable of preserving the positive, the bounded, and the temporally and spatially monotone characters of initial approximations; moreover, we establish that the method is conditionally stable under suitable constraints on the model and numerical parameters. Some simulations are provided to evince the validity of our analytical results. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013