An economic method for the approximate solution of Laplace's difference equation in rectangular regions

✍ Scribed by C.E. Romanova

• Publisher: Elsevier Science
• Year: 1983
• Weight: 524 KB
• Volume: 23
• Category: Article
• ISSN: 0041-5553
• DOI: 10.1016/s0041-5553(83)80106-2

✦ Synopsis

An approximate method of solving Laplace's difference equation in a rectangle with uniform accuracy O(hr) is proposed. Five-point and nine-point Laplace difference operators, boundary conditions of the first and second kinds, and the problem of the contact between two media are considered.

The method can be generalized to the three-dimensional case.

To find an approximate solution, 0(I) arithmetic operations are required for each node of the net.

The main ideas of the method proposed below were presented in /i/.

i. Description of the method.

Suppose [l={(x, y): 0<x<a, 0<y<b}, Ft (l=i, 2, 3, 4) are the sides of a rectangle If, numbered in an anticlockwise direction beginning with the lowest side, with the exception of the ends