A New Methodology for the Development of Efficient Multistep Methods for First-Order Initial Value Problems with Oscillating Solutions: III the Role of the Derivative of the Phase Lag and the Derivative of the Amplification Factor

被引:1
作者
Simos, Theodore E. [1 ,2 ,3 ]
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] Democritus Univ Thrace, Dept Civil Engn, Sect Math, Xanthi 67100, Greece
关键词
numerical solution; initial value problems (IVPs); Adams-Bashforth methods; trigonometric fitting; multistep methods; RUNGE-KUTTA METHOD; NUMERICAL-SOLUTION; INTEGRATION; CONSTRUCTION; STIFF;
D O I
10.3390/axioms13080514
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Recently, the author developed a theory for the computation of the phase lag and amplification factor for explicit and implicit multistep methods for first-order differential equations. In this paper, we will investigate the role of the derivatives of the phase lag and the derivatives of the amplification factor on the efficiency of the newly developed methods. We will also present the stability regions of the newly developed methods. We will also present numerical experiments and conclusions on the newly developed methodologies.
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页数:39
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