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The eighth order Numerov method

✍ Scribed by J.P Killingbeck; G Jolicard

Book ID
104337623
Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
48 KB
Volume
261
Category
Article
ISSN
0375-9601

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✦ Synopsis

A comparison of the shooting and the matrix diagonalization forms of the finite difference method for the Schrodinger Γ«quation leads to an order doubling principle which produces an eigenvalue estimate of 8th order from the traditional Numerov method. Some specimen calculations are given, and a discussion is given of some subtle points concerning the order of approximation of various energy contributions and the effect of varying the choice of the wavefunction at external points.

πŸ“œ SIMILAR VOLUMES

Symbolic derivation of order conditions
Symbolic derivation of order conditions for hybrid Numerov-type methods solving
✍ I.Th. Famelis; Ch. Tsitouras πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 238 KB

Numerov-type ODE solvers are widely used for the numerical treatment of second-order initial value problems. In this work we present a powerful and efficient symbolic code in MATHEMATICA for the derivation of their order conditions and principal truncation error terms. The relative tree theory for s