An almost fourth order uniformly convergent domain decomposition method for a coupled system of singularly perturbed reaction-diffusion equations

作者：Rao S Chandra Sekhara^*; Kumar Sunil

来源：Journal of Computational and Applied Mathematics, 2011, 235(11): 3342-3354.

DOI：10.1016/j.cam.2011.01.047

• Singular perturbation
• Coupled system
• Uniform convergence
• Domain decomposition
• High order

We consider a system of M(>= 2) singularly perturbed equations of reaction-diffusion type coupled through the reaction term. A high order Schwarz domain decomposition method is developed to solve the system numerically. The method splits the original domain into three overlapping subdomains. On two boundary layer subdomains we use a compact fourth order difference scheme on a uniform mesh while on the interior subdomain we use a hybrid scheme on a uniform mesh. We prove that the method is almost fourth order e-uniformly convergent. Furthermore, we prove that when E is small, one iteration is sufficient to get almost fourth order E-uniform convergence. Numerical experiments are performed to support the theoretical results.

• 出版日期2011-4-1