Difference methods on a digital computer for laplacian boundary value and eigenvalue problems
β Scribed by George E. Forsythe
- Publisher
- John Wiley and Sons
- Year
- 1956
- Tongue
- English
- Weight
- 558 KB
- Volume
- 9
- Category
- Article
- ISSN
- 0010-3640
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β¦ Synopsis
P, not in the open region R. For any such point P, let S, denote the closed segment of the net joining P to P, . For each k = 1, * * , 9, the point of S, n C closest to P will be called a boundary fioint of the net. The set of boundary points will be denoted b y C, . Some points of C, may be nodes, but each irregular interior point of R, has one or more neighboring points in C, which are not nodes. (The definition of C, given in [2], although intended to be the same, is not precise.) s1 5 s 5 s, , * * * , St-1 5 s 5 S t .
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We present new finite difference methods of order at most O(hh) for computing eigenvalues of two-point boundary value problems. Our methods lead to generalized seven-band matrix eigenvalue problems. Some typical boundary value problems are treated numerically and these numerical results are summariz