A new multistep method with optimized characteristics for initial and/or boundary value problems

作者：Qiu, Guo-Hua; Liu, Chenglian; Simos, T. E.^*

来源：Journal of Mathematical Chemistry, 2019, 57(1): 119-148.

DOI：10.1007/s10910-018-0940-3

• Phase-lag
• Derivative of the phase-lag
• Initial value problems
• Oscillating solution
• Symmetric
• Hybrid
• Multistep
• Schrodinger equation
• 65L05

In this paper we introduce, for the first time in the literature, an optimized multistage symmetric two-step method. This method is considered as optimized due to the following reasons: (1) it is of tenth-algebraic order scheme, (2) it has obliterated the phase-lag and its first, second, third and fourth derivatives, (3) it has improved stability characteristics, (4) it is a P-stable method. For the new proposed multistage symmetric two-step method we present a full theoretical investigation consisted of: (1) local truncation error and comparative error analysis, (2) stability analysis and (3) interval of periodicity analysis. The effectiveness of the new builded multistage symmetric two-step method is evaluated on the solution of systems of coupled differential equations of the Schrodinger type.

• 出版日期2019-1
• 单位福建师范大学