Stability of Runge-Kutta Methods for Neutral Delay Differential Equations

This paper is concerned with the numerical stability of a class of nonlinear neutral delay differential equations. The numerical stability results are obtained for(k,l)-algebraically stable Runge-Kutta methods when they are applied to this type of problem. Numerical examples are given to confirm our theoretical results.

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The Properties of Multistep Runge-Kutta Methods for Neutral Delay Differential Equations

Software Engineering and Algorithms - Lecture Notes in Networks and Systems ◽

10.1007/978-3-030-77442-4_57 ◽

2021 ◽

pp. 682-700

Author(s):

Kewei Zhang ◽

Haiyan Yuan

Keyword(s):

Differential Equations ◽

Delay Differential Equations ◽

Neutral Delay ◽

Neutral Delay Differential Equations ◽

Runge Kutta ◽

Delay Differential

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Dependence Analysis of the Solutions on the Parameters of Fractional Neutral Delay Differential Equations

Advances in Applied Mathematics and Mechanics ◽

10.4208/aamm.2013.m436 ◽

2016 ◽

Vol 8 (5) ◽

pp. 772-783

Author(s):

Shuiping Yang

Keyword(s):

Theoretical Analysis ◽

Differential Equations ◽

Delay Differential Equations ◽

Initial Function ◽

Hand Function ◽

Dependence Analysis ◽

Neutral Delay ◽

Neutral Delay Differential Equations ◽

Delay Differential ◽

Theoretical Results

AbstractIn this paper, we discuss the dependence of the solutions on the parameters (order, initial function, right-hand function) of fractional neutral delay differential equations (FNDDEs). The corresponding theoretical results are given respectively. Furthermore, we present some numerical results that support our theoretical analysis.

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Numerical stability of one-leg methods for neutral delay differential equations

BIT Numerical Mathematics ◽

10.1007/s10543-011-0352-2 ◽

2011 ◽

Vol 52 (1) ◽

pp. 251-269 ◽

Cited By ~ 7

Author(s):

Liping Wen ◽

Xiong Liu

Keyword(s):

Differential Equations ◽

Delay Differential Equations ◽

Numerical Stability ◽

Neutral Delay ◽

Neutral Delay Differential Equations ◽

Delay Differential

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Stability of continuous Runge–Kutta-type methods for nonlinear neutral delay-differential equations

Applied Mathematical Modelling ◽

10.1016/j.apm.2008.10.038 ◽

2009 ◽

Vol 33 (8) ◽

pp. 3319-3329 ◽

Cited By ~ 35

Author(s):

Wansheng Wang ◽

Yuan Zhang ◽

Shoufu Li

Keyword(s):

Differential Equations ◽

Delay Differential Equations ◽

Neutral Delay ◽

Neutral Delay Differential Equations ◽

Runge Kutta ◽

Delay Differential

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Nonlinear Stability and Convergence of Two-Step Runge-Kutta Methods for Neutral Delay Differential Equations

Mathematical Problems in Engineering ◽

10.1155/2013/683137 ◽

2013 ◽

Vol 2013 ◽

pp. 1-14 ◽

Cited By ~ 2

Author(s):

Haiyan Yuan ◽

Cheng Song ◽

Peichen Wang

Keyword(s):

Differential Equations ◽

Nonlinear Stability ◽

Delay Differential Equations ◽

Stability And Convergence ◽

Neutral Delay ◽

Neutral Delay Differential Equations ◽

Restricted Type ◽

Runge Kutta ◽

The Stability ◽

Delay Differential

This paper is devoted to the stability and convergence analysis of the two-step Runge-Kutta (TSRK) methods with the Lagrange interpolation of the numerical solution for nonlinear neutral delay differential equations. Nonlinear stability and D-convergence are introduced and proved. We discuss theGR(l)-stability,GAR(l)-stability, and the weakGAR(l)-stability on the basis of(k,l)-algebraically stable of the TSRK methods; we also discuss the D-convergence properties of TSRK methods with a restricted type of interpolation procedure.

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Wavelet collocation methods for solving neutral delay differential equations

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2020-0103 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Mo Faheem ◽

Akmal Raza ◽

Arshad Khan

Keyword(s):

Differential Equations ◽

Delay Differential Equations ◽

Series Solution ◽

Collocation Methods ◽

Proportional Delay ◽

Neutral Delay ◽

Neutral Delay Differential Equations ◽

Runge Kutta ◽

Delay Differential ◽

Wavelet Series

Abstract In this paper, we proposed wavelet based collocation methods for solving neutral delay differential equations. We use Legendre wavelet, Hermite wavelet, Chebyshev wavelet and Laguerre wavelet to solve the neutral delay differential equations numerically. We solved five linear and one nonlinear problem to demonstrate the accuracy of wavelet series solution. Wavelet series solution converges fast and gives more accurate results in comparison to other methods present in literature. We compare our results with Runge–Kutta-type methods by Wang et al. (Stability of continuous Runge–Kutta-type methods for nonlinear neutral delay-differential equations,” Appl. Math. Model, vol. 33, no. 8, pp. 3319–3329, 2009) and one-leg θ methods by Wang et al. (Stability of one-leg θ method for nonlinear neutral differential equations with proportional delay,” Appl. Math. Comput., vol. 213, no. 1, pp. 177–183, 2009) and observe that our results are more accurate.

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Stepsize Restrictions for Nonlinear Stability Properties of Neutral Delay Differential Equations

Abstract and Applied Analysis ◽

10.1155/2014/304071 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7

Author(s):

Wei Gu ◽

Ming Wang ◽

Dongfang Li

Keyword(s):

Numerical Methods ◽

Differential Equations ◽

Nonlinear Stability ◽

Delay Differential Equations ◽

Neutral Delay ◽

Stability Properties ◽

Neutral Delay Differential Equations ◽

Runge Kutta ◽

Delay Differential ◽

The Relationship

The present paper is concerned with the relationship between stepsize restriction and nonlinear stability of Runge-Kutta methods for delay differential equations. We obtain a special stepsize condition guaranteeing global and asymptotical stability properties of numerical methods. Some confirmations of the conditions on Runge-Kutta methods are illustrated at last.

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