On the positivity, monotonicity, and stability of a semi-adaptive LOD method for solving three-dimensional degenerate Kawarada equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:439

Article

Padgett, Joshua L.¹ 

[1] Baylor Univ, Dept Math, One Bear Pl, Waco, TX 76798 USA

关键词: Kawarada equations;    Quenching singularity;    Degeneracy;    Nonuniform grids;    Temporal adaptation;    Splitting method;   

DOI  :  10.1016/j.jmaa.2016.02.071

来源: Elsevier

【 摘 要 】

This paper concerns the numerical solution of three-dimensional degenerate Kawarada equations. These partial differential equations possess highly nonlinear source terms, and exhibit strong quenching singularities which pose severe challenges to the design and analysis of highly reliable schemes. Arbitrary fixed nonuniform spatial grids, which are not necessarily symmetric, are considered throughout this study. The numerical solution is advanced through a semi-adaptive Local One-Dimensional (LOD) integrator. The temporal adaptation is achieved via a suitable arc-length monitoring mechanism. Criteria for preserving the positivity and monotonicity are investigated and acquired. The numerical stability of the splitting method is proven in the von Neumann sense under the spectral norm. Extended stability expectations are proposed and investigated. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free