We determine optimal stability polynomials p(x) for splitting method solutions of differential equations, building on previous work by L6pez-Marcos, Sanz-Sema and Skeel (1996). The methods have a variety of stage numbers and are up to eighth order. Knowledge of p(x) allows construction of the most s
Splitting methods for the time-dependent Schrödinger equation
✍ Scribed by S. Blanes; P.C. Moan
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 135 KB
- Volume
- 265
- Category
- Article
- ISSN
- 0375-9601
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✦ Synopsis
Cheap and easy to implement fourth-order methods for the Schrodinger equation with time-dependent Hamiltonians are ïntroduced.
The methods require evaluations of exponentials of simple unidimensional integrals, and can be considered an averaging technique, preserving many of the qualitative properties of the exact solution.
📜 SIMILAR VOLUMES
The Lagrange Manifold (WKB) formalism enables the determination of the asymptotic series solution of linear hyperbolic and parabolic differential equations at turning points. Here this formalism is applied to determine the asymptotic solution of the time-dependent SchrSdinger equation at turning poi