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Keywords:

  • Burgers-Fisher equation;
  • finite-difference scheme;
  • boundedness;
  • monotonicity;
  • nonlinear stability

Abstract

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