Convergence and Stability in Collocation Methods of Equation u′(t) = au(t) plus bu([t])

被引：1

作者：

Yan, Han ^{[1
]}

Ma, Shufang ^{[2
]}

Liu, Yanbin ^{[1
]}

Sun, Hongquan ^{[1
]}

机构：

[1] Heilongjiang Univ, Sch Math Sci, Harbin 150080, Peoples R China

[2] NE Forest Univ, Dept Math, Harbin 150040, Peoples R China

来源：

JOURNAL OF APPLIED MATHEMATICS | 2012年

关键词：

RUNGE-KUTTA METHODS; DIFFERENTIAL-EQUATIONS; NUMERICAL-SOLUTION; DELAYS;

D O I：

10.1155/2012/125926

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the convergence, global superconvergence, local superconvergence, and stability of collocation methods for u'(t) = au(t) + bu([t]). The optimal convergence order and superconvergence order are obtained, and the stability regions for the collocation methods are determined. The conditions that the analytic stability region is contained in the numerical stability region are obtained, and some numerical experiments are given.

引用

页数：17

共 50 条

[1] Stability of Euler-Maclaurin Methods in the Numerical Solution of Equation u′(t) = au(t) plus a0u([t]) plus a1u([t-1])
He, Chunyan
Lv, Wanjin
INFORMATION COMPUTING AND APPLICATIONS, PT 1, 2010, 105 : 62 - 69
[2] Stability analysis of Runge-Kutta methods for systems u'(t) = Lu(t) plus Mu([t])
Liang, Hui
Liu, M. Z.
Yang, Z. W.
APPLIED MATHEMATICS AND COMPUTATION, 2014, 228 : 463 - 476
[3] Oscillation of numerical solution in the Runge-Kutta methods for equation x'(t) = ax(t) plus a 0 x([t])
Wang, Qi
Qiu, Shen-shan
ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2014, 30 (04): : 943 - 950
[4] Numerical stability and oscillation of the Runge-Kutta methods for equation x′(t) = ax(t) plus a0x(M[t plus N/M])
Song, Minghui
Liu, M. Z.
ADVANCES IN DIFFERENCE EQUATIONS, 2012,
[5] Preservation of oscillations of the Runge-Kutta method for equation x′(t) plus ax(t) plus a1x([t-1])=0
Liu, M. Z.
Gao, J. F.
Yang, Z. W.
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2009, 58 (06) : 1113 - 1125
[6] Oscillation of Numerical Solution in the Runge-Kutta Methods for Equation x'(t)=ax(t)+a0x([t])
Qi WANG
Shen-shan QIU
Acta Mathematicae Applicatae Sinica, 2014, 30 (04) : 943 - 950
[7] Oscillation of numerical solution in the Runge-Kutta methods for equation x′(t) = ax(t) + a0x([t])
Qi Wang
Shen-shan Qiu
Acta Mathematicae Applicatae Sinica, English Series, 2014, 30 : 943 - 950
[8] Explicit, ninth order, two step methods for solving inhomogeneous linear problems x"(t) = Λx(t) plus f(t)
Simos, T. E.
Tsitouras, Ch
APPLIED NUMERICAL MATHEMATICS, 2020, 153 : 344 - 351
[9] Oscillation analysis of numerical solution in the θ-methods for equation x′(t)+ax(t)+a1x([t-1])=0
Liu, M. Z.
Gao, Jianfang
Yang, Z. W.
APPLIED MATHEMATICS AND COMPUTATION, 2007, 186 (01) : 566 - 578
[10] Convergence and stability of spectral collocation method for hyperbolic partial differential equation with piecewise continuous arguments
Chen, Yongtang
Wang, Qi
COMPUTATIONAL & APPLIED MATHEMATICS, 2022, 41 (08)

← 1 2 3 4 5 →