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].
Nauja išreikštinė baigtinių skirtumų schema diferencialinių lygčių dalinėmis išvestinėmis sprendimui
Santrauka. Daugelio išreikštųjų baigtinių skirtumų schemų stabilumo reikalavimai yra labai griežti. Darbe nagrinėjamas metodas, kuris jau buvo panaudotas sprendžiant skysčių tekėjimo uždavinius. Parodyta, kad skaitinio algoritmo realizacija yra ekonomiška ir šis metodas gali būti naudojamas sprendžiant plačia nestacionarių uždavinių klasę. Įrodyta, kad naujosios išreikštinės baigtinių skirtumų schemos stabilumo sąlyga yra silpnesnė nei daugelio kitų populiarių išreikštinių skirtumų schemų. Pateikti skaičiavimo eksperimento rezultatai, kai sprendžiama Burgerso lygtis ir Eulerio lygčių sistema.
Dey, S. K. (1999). A novel explicit finite difference scheme for partial differential equations. Mathematical Modelling and Analysis, 4(1), 70-78. https://doi.org/10.3846/13926292.1999.9637112
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