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A family of eight-step methods with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation. (English) Zbl 1217.65143
Summary: A family of tenth algebraic order eight-step methods is constructed in this paper. For this family of methods, we require the phase-lag and its first, second and third derivatives to be vanished. Three alternative methods are proposed which satisfy the above requirements. An error analysis and a stability analysis is also investigated in this paper and a comparison with other methods is also studied. The new proposed methods are applied for the numerical solution of the one dimensional Schrödinger equation. The efficiency of the new methodology is proved via theoretical analysis and numerical applications.
MSC:
65L06Multistep, Runge-Kutta, and extrapolation methods
References:
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[78]Avdelas G., Konguetsof A., Simos T.E.: A family of hybrid eighth order methods with minimal phase-lag for the numerical solution of the Schrödinger equation and related problems. Int. J. Mod. Phys. C 11, 415–437 (2000)
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[84]Simos T.E., Vigo-Aguiar J.: On the construction of efficient methods for second order IVPs with oscillating solution. Int. J. Mod. Phys. C 12, 1453–1476 (2001) · doi:10.1142/S0129183101002826
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[87]Tsitouras Ch., Simos T.E.: High algebraic, high phase-lag order embedded Numerov-type methods for oscillatory problems. Appl. Math. Comput. 131, 201–211 (2002) · Zbl 1021.65036 · doi:10.1016/S0096-3003(01)00133-3
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