An almost third order finite difference scheme for singularly perturbed reaction-diffusion systems

作者：Clavero C^*; Gracia J L; Li**ona F J

来源：Journal of Computational and Applied Mathematics, 2010, 234(8): 2501-2515.

DOI：10.1016/j.cam.2010.03.011

• Reaction-diffusion systems
• High order
• Uniform convergence
• Shishkin mesh
• Hybrid HODIE methods

This paper addresses the numerical approximation of solutions to coupled systems of singularly perturbed reaction-diffusion problems. In particular a hybrid finite difference scheme of HODIE type is constructed on a piecewise uniform Shishkin mesh. It is proved that the numerical scheme satisfies a discrete maximum principle and also that it is third order (except for a logarithmic factor) uniformly convergent, even for the case in which the diffusion parameter associated with each equation of the system has a different order of magnitude. Numerical examples supporting the theory are given.

• 出版日期2010-8-15