FD-method for an eigenvalue problem with nonlinear potential

被引：0
作者：
Havrylyuk I.P. [1 ,2 ]
Klymenko A.V. [1 ,2 ]
Makarov V.L. [1 ,2 ]
Rossokhata N.O. [1 ,2 ]
机构：
[1] Professional Academy, Eisenach
[2] Institute of Mathematics, Ukrainian Academy of Sciences, Kyiv
来源：
Ukrainian Mathematical Journal | 2007年 / 59卷 / 1期
关键词：
Eigenvalue Problem; Order Number; Shooting Method; Exponential Rate; Linear Component;
D O I：
10.1007/s11253-007-0002-7
中图分类号：
学科分类号：
摘要：
Using the functional discrete approach and Adomian polynomials, we propose a numerical algorithm for an eigenvalue problem with a potential that consists of a nonlinear autonomous part and a linear part depending on an independent variable. We prove that the rate of convergence of the algorithm is exponential and improves as the order number of an eigenvalue increases. We investigate the mutual influence of the piecewise-constant approximation of the linear part of the potential and the nonlinearity on the rate of convergence of the method. Theoretical results are confirmed by numerical data. © Springer Science+Business Media, Inc. 2007.
引用
收藏
页码：12 / 27
页数：15
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