Efficient Splitting Methods Based on Modified Potentials: Numerical Integration of Linear Parabolic Problems and Imaginary Time Propagation of the Schrodinger Equation
[EN] We present a new family of fourth-order splitting methods with positive co-efficients especially tailored for the time integration of linear parabolic problems and, in particular, for the time dependent Schrodinger equation, both in real and imaginary time. They are based on the use of a double...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/212320 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/212320 |
| Access Level: | acceso abierto |
| Palabra clave: | Schrodinger equation Imaginary time propagation Parabolic equations Operator splitting methods Modified potentials MATEMATICA APLICADA |
| Sumario: | [EN] We present a new family of fourth-order splitting methods with positive co-efficients especially tailored for the time integration of linear parabolic problems and, in particular, for the time dependent Schrodinger equation, both in real and imaginary time. They are based on the use of a double commutator and a modified processor, and are more efficient than other widely used schemes found in the literature. Moreover, for certain potentials, they achieve order six. Several examples in one, two and three dimensions clearly illustrate the computational advantages of the new schemes. |
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