Explicit finite difference schemes adapted to advection-reaction equations

Authors:
J. Martín-Vaquero;J. Vigo-Aguiar
Affiliations:
Scientific Computing Group, Facultad de Ciencias, Universidad de Salamanca, Salamanca, Spain;Scientific Computing Group, Facultad de Ciencias, Universidad de Salamanca, Salamanca, Spain
Venue:
International Journal of Computer Mathematics - Recent Advances in Computational and Applied Mathematics in Science and Engineering
Year:
2008

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Abstract

Several numerical methods are presented that have been adapted for a linear, first-order, hyperbolic partial differential equation-the non-homogeneous constant coefficient one-way advection-reaction equation. This equation is solved exactly when the non-homogeneous part is a polynomial in time and/or space. The convergence properties of stability and consistency are analysed when these schemes are applied to this equation. Finally, it is shown that these methods produce very good results when applied to other nonlinear problems.