The stability of natural Runge-Kutta methods for nonlinear delay differential equations

Toshiyuki Koto

doi:10.1007/bf03167314

The stability of natural Runge-Kutta methods for nonlinear delay differential equations

Japan Journal of Industrial and Applied Mathematics ◽

10.1007/bf03167314 ◽

1997 ◽

Vol 14 (1) ◽

pp. 111-123 ◽

Cited By ~ 6

Author(s):

Toshiyuki Koto

Keyword(s):

Differential Equations ◽

Delay Differential Equations ◽

Nonlinear Delay Differential Equations ◽

Runge Kutta ◽

The Stability ◽

Delay Differential ◽

Nonlinear Delay

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Stability and Dissipativity of Multistep Runge–Kutta Methods for Nonlinear Delay Differential Equations with Constrained Grid

Computational Statistics and Mathematical Modeling Methods in Intelligent Systems - Advances in Intelligent Systems and Computing ◽

10.1007/978-3-030-31362-3_23 ◽

2019 ◽

pp. 227-242

Author(s):

Yuhuan Fan ◽

Haiyan Yuan ◽

Peichen Wang

Keyword(s):

Differential Equations ◽

Delay Differential Equations ◽

Nonlinear Delay Differential Equations ◽

Runge Kutta ◽

Delay Differential ◽

Nonlinear Delay

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Exponential Decay Estimates For Some Components of Solutions to the Nonlinear Delay Differential Equations of the Living System Models

Siberian Mathematical Journal ◽

10.1134/s0037446620040126 ◽

2020 ◽

Vol 61 (4) ◽

pp. 715-724

Author(s):

N. V. Pertsev

Keyword(s):

Differential Equations ◽

Exponential Decay ◽

Delay Differential Equations ◽

Living System ◽

Decay Estimates ◽

System Models ◽

Nonlinear Delay Differential Equations ◽

Delay Differential ◽

Nonlinear Delay

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Oscillatory behavior of solutions of odd-order nonlinear delay differential equations

Advances in Difference Equations ◽

10.1186/s13662-020-02821-8 ◽

2020 ◽

Vol 2020 (1) ◽

Cited By ~ 1

Author(s):

Osama Moaaz

Keyword(s):

Differential Equations ◽

Delay Differential Equations ◽

Oscillatory Behavior ◽

Odd Order ◽

Nonlinear Delay Differential Equations ◽

Delay Differential ◽

Nonlinear Delay

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An efficient numerical algorithm for solution of nonlinear delay differential equations

Journal of Physics Conference Series ◽

10.1088/1742-6596/1849/1/012014 ◽

2021 ◽

Vol 1849 (1) ◽

pp. 012014

Author(s):

Anil Kumar ◽

Giriraj Methi

Keyword(s):

Differential Equations ◽

Numerical Algorithm ◽

Delay Differential Equations ◽

Nonlinear Delay Differential Equations ◽

Delay Differential ◽

Nonlinear Delay

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Global solutions of a singular initial value problem to second order nonlinear delay differential equations

Mathematical and Computer Modelling ◽

10.1016/j.mcm.2005.12.005 ◽

2006 ◽

Vol 43 (7-8) ◽

pp. 854-869 ◽

Cited By ~ 8

Author(s):

R.P. Agarwal ◽

Ch.G. Philos ◽

P.Ch. Tsamatos

Keyword(s):

Differential Equations ◽

Initial Value Problem ◽

Delay Differential Equations ◽

Global Solutions ◽

Second Order ◽

Initial Value ◽

Singular Initial Value Problem ◽

Nonlinear Delay Differential Equations ◽

Delay Differential ◽

Nonlinear Delay

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On the stability of adaptations of Runge-Kutta methods to systems of delay differential equations

Applied Numerical Mathematics ◽

10.1016/s0168-9274(96)00035-9 ◽

1996 ◽

Vol 22 (1-3) ◽

pp. 237-250 ◽

Cited By ~ 11

Author(s):

K.J. in 't Hout

Keyword(s):

Differential Equations ◽

Delay Differential Equations ◽

Runge Kutta ◽

The Stability ◽

Delay Differential

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Three positive solutions to initial-boundary value problems of nonlinear delay differential equations

Electronic journal of qualitative theory of differential equations ◽

10.14232/ejqtde.2009.1.14 ◽

2009 ◽

pp. 1-11

Author(s):

Yuming Wei ◽

Patricia J. Y. Wong

Keyword(s):

Differential Equations ◽

Boundary Value Problems ◽

Positive Solutions ◽

Delay Differential Equations ◽

Initial Boundary ◽

Initial Boundary Value Problems ◽

Nonlinear Delay Differential Equations ◽

Initial Boundary Value ◽

Delay Differential ◽

Nonlinear Delay

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Nonlinear delay differential equations involving population growth

Mathematical and Computer Modelling ◽

10.1016/j.mcm.2003.09.038 ◽

2004 ◽

Vol 40 (5-6) ◽

pp. 583-590 ◽

Cited By ~ 11

Author(s):

Y. Lenbury ◽

D.V. Giang

Keyword(s):

Differential Equations ◽

Population Growth ◽

Delay Differential Equations ◽

Nonlinear Delay Differential Equations ◽

Delay Differential ◽

Nonlinear Delay

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Stability of nonlinear delay differential equations with impulses☆

Nonlinear Analysis ◽

10.1016/s0362-546x(04)00266-4 ◽

2004 ◽

Vol 59 (4) ◽

pp. 453-464

Author(s):

X ZHANG ◽

J YAN

Keyword(s):

Differential Equations ◽

Delay Differential Equations ◽

Nonlinear Delay Differential Equations ◽

Delay Differential ◽

Nonlinear Delay

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Oscillation and asymptotic behavior of third-order nonlinear delay differential equations with positive and negative terms

Applied Mathematics Letters ◽

10.1016/j.aml.2022.107927 ◽

2022 ◽

pp. 107927

Author(s):

Xun-Huan Deng ◽

Xianyong Huang ◽

Qi-Ru Wang

Keyword(s):

Asymptotic Behavior ◽

Differential Equations ◽

Delay Differential Equations ◽

Third Order ◽

Nonlinear Delay Differential Equations ◽

Delay Differential ◽

Nonlinear Delay

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