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A compound adaptive approach to degenerate nonlinear quenching problems
Author(s) -
Sheng Q.,
Khaliq A. Q. M.
Publication year - 1999
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/(sici)1098-2426(199901)15:1<29::aid-num2>3.0.co;2-l
Subject(s) - degenerate energy levels , quenching (fluorescence) , mathematics , solver , monotone polygon , nonlinear system , convergence (economics) , computation , degeneracy (biology) , ode , mathematical optimization , algorithm , physics , geometry , quantum mechanics , fluorescence , bioinformatics , economics , biology , economic growth
Quenching phenomena play important roles in both steady and unsteady combustion processes. This article studies a compound finite difference method for solving a nonlinear degenerate combustion model problem. The approach combines procedures of semidiscretization, adaptive ODE solver, and highly stable rational approximation for handling the spatial degeneracy and quenching singularity involved. A second‐order adaptive scheme is constructed, which provides monotone convergence of the numerical solution and direct computations of critical quenching values. It has a simple, yet accurate and reliable, structure and is easy to use. We further demonstrate advantages of the scheme by comparing it to existing algorithms. Numerical examples are presented to further strengthen our results. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 29–47, 1999