A New Methodology for the Development of Efficient Multistep Methods for First-Order IVPs with Oscillating Solutions

被引：7
|
作者：
Simos, Theodore E. [1 ,2 ,3 ,4 ,5 ,6 ]
机构：
[1] Hangzhou Dianzi Univ, Sch Mech Engn, Er Hao Da Jie 1158, Hangzhou 310018, Peoples R China
[2] Gulf Univ Sci & Technol, Ctr Appl Math & Bioinformat, West Mishref 32093, Kuwait
[3] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung 40402, Taiwan
[4] Ulyanovsk State Tech Univ, Lab Interdisciplinary Problems Energy Prod, 32 Severny Venetz St, Ulyanovsk 432027, Russia
[5] Neijiang Normal Univ, Data Recovery Key Lab Sichuan Prov, Dongtong Rd 705, Neijiang 641100, Peoples R China
[6] Democritus Univ Thrace, Dept Civil Engn, Sect Math, Xanthi 67100, Greece
来源：
MATHEMATICS | 2024年 / 12卷 / 04期
关键词：
numerical solution; initial value problems (IVPs); Adams-Bashforth methods; trigonometric fitting; multistep methods; RUNGE-KUTTA METHODS; EXPONENTIAL-FITTING METHODS; INITIAL-VALUE PROBLEMS; 2-STEP HYBRID METHODS; TRIGONOMETRICALLY-FITTED METHOD; EXPLICIT ARKN METHODS; NOUMEROV-TYPE METHOD; NUMEROV-TYPE METHOD; MINIMAL PHASE-LAG; P-STABLE METHODS;
D O I：
10.3390/math12040504
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this research, we provide a novel approach to the development of effective numerical algorithms for the solution of first-order IVPs. In particular, we detail the fundamental theory behind the development of the aforementioned approaches and show how it can be applied to the Adams-Bashforth approach in three steps. The stability of the new scheme is also analyzed. We compared the performance of our novel algorithm to that of established approaches and found it to be superior. Numerical experiments confirmed that, in comparison to standard approaches to the numerical solution of Initial Value Problems (IVPs), including oscillating solutions, our approach is significantly more effective.
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页数：32
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