Fully implicit finite differences methods for two-dimensional diffusion with a non-local boundary condition

✍ Scribed by Mehdi Dehghan

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 616 KB
• Volume: 106
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/s0377-0427(99)00065-5

✦ Synopsis

Three new fully implicit methods which are based on the (5,5) Crank-Nicolson method, the (5,5) N-H (Noye-Hayman) implicit method and the (9,9) N-H implicit method are developed for solving the heat equation in two dimensional space with non-local boundary conditions. The latter is fourth-order while the others are second-order. While the implicit methods developed here, like the scheme based on the standard implicit backward time centered space (BTCS) method, use a large amount of central processor (CPU) time, the high accuracy of the new fourth-order fully implicit scheme is significant. Like the BTCS method, the new methods are also unconditionally stable.