An accurate eighth order exponentially-fitted method for the efficient solution of the Schrödinger equation. (English) Zbl 0976.65060
This paper constructs an eighth-order exponentially fitted method for solving differential equations arising from the Schrödinger equation. A comprehensive order and truncation error analysis is given using MAPLE. A variable stepsize implementation is introduced and compared with existant methods on some simple problems.
Reviewer: Kevin Burrage (Brisbane)
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65L50 | Mesh generation, refinement, and adaptive methods for ordinary differential equations |
| 65L70 | Error bounds for numerical methods for ordinary differential equations |
| 34L40 | Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) |
