Open AccessA NOVEL EXPLICIT FINITE DIFFERENCE SCHEME FOR PARTIAL DIFFERENTIAL EQUATIONS
Author(s) -
S. K. Dey
Publication year - 1999
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.1999.9637112
Subject(s) - mathematics , partial differential equation , finite difference , simple (philosophy) , stability (learning theory) , finite difference method , flow (mathematics) , scheme (mathematics) , fluid dynamics , finite difference scheme , finite difference coefficient , differential equation , mathematical analysis , finite element method , computer science , mixed finite element method , geometry , philosophy , physics , epistemology , machine learning , mechanics , thermodynamics
Most explicit finite difference schemes have very stringent stability criterion. In 1982, Charlie Dey [1] developed a novel method and solved several partial differential equations representing models of fluid flow. (He was then only 10 years old). Recent mathematical analysis shows that this relatively simple method is quite powerful to solve any flow model if it has a steady‐state solution using a stability criterion which is a lot less stringent than most explicit finite difference schemes generally applied in Computational Fluid Dynamics [2].