An Implicit Pseudospectral Scheme to Solve Propagating Fronts in Reaction-Diffusion Equations

作者：Olmos Liceaga Daniel^*; Segundo Caballero Israel

来源：Numerical Methods for Partial Differential Equations, 2016, 32(1): 86-105.

DOI：10.1002/num.21985

• Chebyshev pseudospectral
• implicit method
• reaction-diffusion
• wave-front propagation

Some Reaction-Diffusion equations present solutions of the traveling wave form. In this work, we present an implicit numerical scheme based on finite difference originally proposed to solve hyperbolic equations. Then, this method is improved using a pseudospectral approach to discretize the spatial variable. The results prove that this new scheme is useful to solve equations of the parabolic type which presents traveling wave solutions. In particular, problems where a reduction in the number of discretization points and an increase of the size of the time step play an important role in their solution are considered. The implicit scheme presented involves the solution of linear systems only.

• 出版日期2016-1