An adaptive moving grid method for a system of singularly perturbed initial value problems

作者：Liu, Li Bin; Chen, Yanping^*

来源：Journal of Computational and Applied Mathematics, 2015, 274: 11-22.

DOI：10.1016/j.cam.2014.06.022

• Singularly perturbed
• Initial value problem
• Adaptive grid
• Uniform convergence

A system of first-order singularly perturbed initial value problems is considered. The system is discretized by a backward Euler difference scheme for which a priori error analysis in the maximum norm is constructed. It is shown from the a priori error bound that there exists a mesh with N subintervals that gives optimal error bound of O(N-1) which is robust with respect to the perturbation parameters. A partly heuristic argument based on a priori error analysis leads to a suitable monitor function. Based on an a posteriori error bound, a first-order rate of convergence, independent of all perturbation parameters, is established. A linear and a nonlinear examples are tested, and the numerical results are provided to demonstrate the effectiveness of our adaptive moving grid method.

• 出版日期2015-1-15
• 单位华南师范大学; 池州学院