A new two-step finite difference pair with optimal properties

作者：Zheng, Jinbin; Liu, Chenglian; Simos, T. E.^*

来源：Journal of Mathematical Chemistry, 2018, 56(3): 770-798.

DOI：10.1007/s10910-017-0829-6

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

A new four-stages symmetric two-step finite difference pair with optimal error, phase-lag and general stability properties is obtained, for the first time in the literature, in this paper.
The new scheme has the following properties:
is of symmetric form,
is a two-step finite difference pair,
is of four-stages finite difference pair,
is of tenth-algebraic order,
the approximations which are obtained at each level of the new finite difference scheme are the following:
An approximation obtained on the first level on the point ,
An approximation obtained on the second level on the point ,
An approximation obtained on the third level on the point and finally,
An approximation obtained on the fourth (final) level on the point ,
it has vanished the phase-lag and its first, second, third, fourth and fifth derivatives,
it has optimized stability properties,
has efficient stability properties since it has an interval of periodicity equal to (0, 9, 2).
For the new four-stages symmetric two-step finite difference pair we present a full theoretical analysis (error and stability analysis).
The evaluation of the efficiency of the new developed four-stages symmetric two-step finite difference pair is based on its application on systems of coupled differential equations of the Schrodinger form.

• 出版日期2018-3
• 单位内江师范学院; 龙岩学院