New Runge-Kutta type symmetric two-step method with optimized characteristics

作者：Yan, Ke; Simos, T. E.^*

来源：Journal of Mathematical Chemistry, 2018, 56(8): 2454-2484.

DOI：10.1007/s10910-018-0899-0

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

In this paper and for the first time in the literature, we build a new hybrid symmetric two-step method with the following properties: (1) the new scheme is of symmetric type, (2) the new scheme is of two-step, (3) the new scheme is of five-stages, (4) the new scheme is of twelfth-algebraic order, (5) the new scheme has eliminated the phase-lag and its first, second, third, fourth and fifth derivatives, (6) the new scheme has improved stability characteristics for the general problems, (7) the new scheme is P-stable [with interval of periodicity equal to ] and (8) the new scheme builded based on the following approximations: the first stage is approximation on the point , @@@ the second stage is approximation on the point , @@@ the third stage is approximation on the point , @@@ the fourth stage is approximation on the point and finally, @@@ the fifth stage is approximation on the point ,. @@@ For the new builded scheme we give a full numerical analysis ( local truncation error and stability analysis). The efficiency of the new builded scheme is examined with the numerical solution of systems of coupled differential equations of the Schrodinger type.

• 出版日期2018-9
• 单位长安大学