Overlapping domain decomposition method for singularly perturbed third order reaction-diffusion problems

• Published in: Ain Shams Engineering Journal Vol. 9; no. 4; pp. 2171 - 2181
• Main Authors: Christy Roja, J., Tamilselvan, A.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.12.2018; Elsevier
• Subjects: Reaction-diffusion equations; Schwarz method; Singularly perturbed problems; Third order ordinary differential equation; Singularly perturbed problems; AMS 65L11; Reaction-diffusion equations; Third order ordinary differential equation; CR G1.7; Schwarz method
• ISSN: 2090-4479; 2090-4495; 2090-4495
• DOI: 10.1016/j.asej.2016.09.018

In this paper, we present an analysis of overlapping Schwarz method for singularly perturbed third order reaction-diffusion problems. The Schwarz method invokes two fine mesh subdomains and one coarse mesh subdomain. On each subdomain we use a standard finite difference operator with a uniform mesh. The numerical approximations generated from the method are shown to be almost second order uniformly convergent. Furthermore we show that for small ε, two iterations are sufficient to achieve the expected accuracy. Numerical examples are presented to support the theoretical results.