Convergence analysis of Richardson extrapolation for a quasilinear singularly perturbed problem with an integral boundary condition on an adaptive grid. (May 2021)

• Record Type: Journal Article
• Authors: Liu, Li-Bin; Yang, Xiu
• Is Part Of: Applied mathematics letters. Volume 115(2021)
• Publication Date: 2021-05
• Subjects: Singularly perturbed -- Adaptive grid -- Richardson extrapolation -- Uniform convergence; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2020.106976
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: The numerical solution of a quasilinear singularly perturbed problem with an integral boundary condition is considered. For discretizing the differential equation, we use the backward Euler formula and for the integral boundary condition the left rectangle formula is constructed on an arbitrary nonuniform mesh. Based on the truncation error analysis and mesh equidistribution principle, a suitable monitor function is chosen to obtain an adaptive grid. Furthermore, the convergence analysis of our discretization scheme on an adaptive grid before and after Richardson extrapolation is carried out, which is shown that the use of Richardson extrapolation improves the uniform accuracy in the discrete maximum norm from first-order to second-order. Finally, some numerical results are given to illustrate the theoretical results.