A Runge-Kutta type implicit high algebraic order two-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of coupled differential equations arising from the Schrodinger equation

作者：Mu, Kenan; Simos, T. E.^*

来源：Journal of Mathematical Chemistry, 2015, 53(5): 1239-1256.

DOI：10.1007/s10910-015-0484-8

• Schrodinger equation
• Multistep methods
• Interval of periodicity
• Phase-lag
• Phase-fitted
• Derivatives of the phase-lag

A Runge-Kutta type (four stages) eighth algebraic order two-step method with phase-lag and its first, second, third and fourth derivatives equal to zero is produced in this paper. We also study the results of elimination of the phase-lag and its derivatives on the efficiency of the method. Our studies consist: (1) the construction of the method, (2) the determination of the local truncation error of the proposed method, (3) the investigation of the local truncation error analysis using the comparison with other similar methods of the literature, (4) the computation of the interval of periodicity (stability interval) of the developed method. For this calculation we use a scalar test equation with frequency different than the frequency of the scalar test equation used for the phase-lag analysis, (5) the definition of the error estimation based on methods with different algebraic orders and (6) the investigation of the effectiveness of the new obtained method studying the numerical solution of the coupled differential equations arising from the Schrodinger equation.

• 出版日期2015-5
• 单位长安大学