Simple numerical method to study traveling‐wave solutions of a diffusive problem with nonlinear advection and reaction. Issue 5 (23rd March 2013)

• Record Type: Journal Article
• Authors: Macias‐Diaz, Jorge; Villa, J.
• Is Part Of: Numerical methods for partial differential equations. Volume 29:Issue 5(2013:Sep.)
• Page Start: 1694
• Page End: 1708
• Publication Date: 2013-03-23
• Subjects: Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.21772
• Languages: English
• ISSNs: 0749-159X

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>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</p> </abstract>