A hybrid type four-step method with vanished phase-lag and its first, second and third derivatives for each level for the numerical integration of the Schrödinger equation. (English) Zbl 1307.65106
Summary: In this paper, we study the effects of the vanishing of the phase-lag and its first, second and third derivatives on the effectiveness of a four-step hybrid type method of sixth algebraic order. As a result of the above described study, a hybrid type of three level four-step method of sixth algebraic order is obtained. We investigate the new produced method theoretically and computationally. The theoretical investigation of the new hybrid method consists of: 0.5 cm
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- the development of the new method.
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- the computation of the local truncation error.
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- the comparison of the local truncation error analysis with other known methods of the same form.
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- the stability analysis.
MSC:
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
| 34B05 | Linear boundary value problems for ordinary differential equations |
| 34L40 | Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
| 65L70 | Error bounds for numerical methods for ordinary differential equations |
Keywords:
Schrödinger equation; multistep methods; hybrid methods; interval of periodicity; phase-lag; derivatives of the phase-lag; numerical examples; local truncation error; stability; resonance problemReferences:
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