The extended generalized Stormer-Cowell methods for second-order delay boundary value problems

被引:12
作者
Li, Cui [1 ]
Zhang, Chengjian [1 ]
机构
[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China
关键词
Delay boundary value problem; Generalized Stormer-Cowell method; Stability; Convergence; Numerical experiment; DIFFERENTIAL-EQUATIONS;
D O I
10.1016/j.amc.2016.09.006
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This paper deals with the numerical solutions of second-order delay boundary value problems (DBVPs). The generalized Stormer-Cowell methods (GSCMs) for second-order initial value problems, proposed by Aceto et al. (2012), are extended to solve the second-order DBVPs. The existence and uniqueness criterion of the methods is derived. It is proved under the suitable conditions that an extended GSCM is stable, and convergent of order p whenever this method has the consistent order p. The numerical examples illustrate efficiency and accuracy of the methods. Moreover, a comparison between the extended GSCMs and the boundary value methods of first-order BVPs is given. The numerical result shows that the extended GSCMs are comparable. (C) 2016 Elsevier Inc. All rights reserved.
引用
收藏
页码:87 / 95
页数:9
相关论文
共 18 条
[1]   PGSCM: A family of P-stable Boundary Value Methods for second-order initial value problems [J].
Aceto, Lidia ;
Ghelardoni, Paolo ;
Magherini, Cecilia .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2012, 236 (16) :3857-3868
[2]   FINITE-DIFFERENCE METHODS FOR BOUNDARY-VALUE-PROBLEMS OF DIFFERENTIAL-EQUATIONS WITH DEVIATING ARGUMENTS [J].
AGARWAL, RP ;
CHOW, YM .
COMPUTERS & MATHEMATICS WITH APPLICATIONS-PART A, 1986, 12 (11) :1143-1153
[3]  
[Anonymous], 2003, Numerical Methods for Delay Differential Equations
[4]  
[Anonymous], 2001, CAMB TRACT MATH
[5]  
Bakke V. L., 1989, Aplikace Matematiky, V34, P1
[6]   A COLLOCATION METHOD FOR BOUNDARY-VALUE-PROBLEMS OF DIFFERENTIAL-EQUATIONS WITH FUNCTIONAL ARGUMENTS [J].
BELLEN, A ;
ZENNARO, M .
COMPUTING, 1984, 32 (04) :307-318
[7]  
Brugnano L., 1998, SOLVING ORDINARY DIF
[8]   NUMERICAL-METHOD TO BOUNDARY-VALUE PROBLEMS FOR 2ND ORDER DELAY DIFFERENTIAL-EQUATIONS [J].
CHOCHOLATY, P ;
SLAHOR, L .
NUMERISCHE MATHEMATIK, 1979, 33 (01) :69-75
[9]  
CRYER CW, 1973, NUMER MATH, V20, P288, DOI 10.1007/BF01407371
[10]  
Dahlquist G., 1978, BIT (Nordisk Tidskrift for Informationsbehandling), V18, P133, DOI 10.1007/BF01931689