On non negative difference analogues of elliptic differential equations

✍ Scribed by Donald Greenspan; P.C. Jain

• Publisher: Elsevier Science
• Year: 1965
• Tongue: English
• Weight: 246 KB
• Volume: 279
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(65)90423-0

✦ Synopsis

Let L be the elliptic differential operator defined on region R by L[u(x, y)] --ux~ + 2b(x, y)u~u + c(x, y)uuu, b ~ O, where b(x, y) and c(x, y) are continuous and bounded on R. At any point (x, y) E R, the ellipticity condition alone implies the existence of a nine point difference operator analogue Lh of L which is of non-negative type. Moreover, Lh is given constructively. For numerical considerations in the large, it is shown to be su~cient that the following inequality be valid: sap ,b(x,y)[< inf [ c(x'y) ] (x,u)en (~,u)eR ]b(x, Y) I "