Mathematics – Numerical Analysis
Scientific paper
2012-03-08
Mathematics
Numerical Analysis
Scientific paper
This paper studies the numerical solution of traveling singular sources problems. A big challenge is the sources move with different speeds. Our work focus on a moving mesh method based on the domain decomposition. A predictor-corrector algorithm is derived to simulate the position of singular sources, which are described by some ordinary differential equations. The whole domain is splitted into several subdomains according to the positions of the sources. The endpoints of each subdomain are two adjacent sources. In each subdomain, moving mesh method is respectively applied. Moreover, the computation of jump $[\dot{u}]$ is avoided and there are only two different cases discussed in the discretization of the PDE. Furthermore, the new method has a desired second-order of the spacial convergence. Numerical examples are presented to illustrate the convergence rates and the efficiency of the method. Blow-up phenomenon is also investigated for various motions of the sources.
Hu Zhicheng
Liang Keiwei
Zhou Xiaoyan
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