 A high order convergent numerical method for singularly perturbed time dependent problems using mesh equidistributionSunil Kumar, Sumit, and Jesus Vigo-Aguiar Mathematics and Computers in Simulation (MATCOM), 2022, vol. 199, issue C, 287-306 Abstract: The purpose of this paper is to introduce a high order convergent numerical method for singularly perturbed time dependent problems using mesh equidistribution. The discretization is based on the backward Euler scheme in time and a high order non-monotone scheme in space. In time direction we consider a uniform mesh, while in spatial direction we construct an adaptive mesh through equidistribution of a monitor function involving appropriate power of the solution’s second derivative. The method is analysed in two steps, splitting the time and space discretization errors. We establish that the method is uniformly convergent with optimal order having order one in time and order four in space. Further, we use the Richardson extrapolation technique for improving the order of convergence from one to two in time. Numerical experiments are presented to confirm the theoretically proven convergence result. Keywords: Singularly perturbed problem; Time dependent problem; Adaptive mesh; High order scheme; Richardson extrapolation; Robust convergence (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:199:y:2022:i:c:p:287-306 DOI: 10.1016/j.matcom.2022.03.025 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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