A new high algebraic order four stages symmetric two-step method with vanished phase-lag and its first and second derivatives for the numerical solution of the Schrodinger equation and related problems

作者：Xi, Xiaopeng; Simos, T. E.^*

来源：Journal of Mathematical Chemistry, 2016, 54(7): 1417-1439.

DOI：10.1007/s10910-016-0627-6

• Phase-lag
• Derivative of the phase-lag
• Initial value problems
• Oscillating solution
• Symmetric
• Hybrid
• Multistep
• Schrodinger equation

A four stages twelfth algebraic order symmetric two-step method with vanished phase-lag and its first and second derivative is developed in this paper for the first time in the literature. More specifically in this paper the following will be investigated: (i) the phase-lag analysis for the development of the new method, (ii) the construction of the new method, (iii) the local truncation error analysis which is based on the radial Schrodinger equation, (iv) the interval of periodicity analysis and the stability analysis which is based on a scalar test equation with frequency not equal with the frequency of the scalar test equation used for the phase-lag analysis, (v) the error estimation procedure based on the algebraic order, (vi) the numerical results from our numerical tests for the study of the efficiency of the new obtained method. The numerical tests are based on the numerical solution of the Schrodinger equation.

• 出版日期2016-8
• 单位长安大学