Variable-step variable-order 3-stage Hermite–Birkhoff–Obrechkoff DDE solver of order 4 to 14

Yagoub, Hemza; Nguyen‐Ba, Truong; Vaillancourt, Rémi

doi:10.1016/j.amc.2011.05.023

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Cited by 2 publications

(3 citation statements)

References 9 publications

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“…3PVS was tested on the vanishing delay problems and results were compared with other available DDE solver that has solved the same problem in [1]. Note that, TOL is the prescribed tolerance, FNC is a total number of function evaluation, MAXERR is a maximum of mixed error test and '-' is no information has been given.…”

Section: Resultsmentioning

confidence: 99%

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Multistep block method for solving vanishing delay differential equations

Majid¹,

Aziz²

2015

AIP Conference Proceedings

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Section: Resultsmentioning

confidence: 99%

“…the formula of the first point 1 n y is then can be obtained by integrating (2) over the interval 1 , n n x x as follows,…”

Section: Introductionmentioning

confidence: 99%

Multistep block method for solving vanishing delay differential equations

Majid¹,

Aziz²

2015

AIP Conference Proceedings

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“…Then for the asymptotically vanishing lag case, they have used the approach of the first case as starter and then the delay equation is approximated by solving it as an ODE. The latest code for the numerical scheme of small, vanishing, and asymptotically vanishing delay in DDEs has come out in Yagoub et al [3] in the name of HBODDE. This code is based on a hybrid variable-step variable-order 3stage Hermite-Birkhoff-Obrechkoff ODE solver that has been adapted in DDEs.…”

Section: Introductionmentioning

confidence: 99%

Solving Delay Differential Equations of Small and Vanishing Lag Using Multistep Block Method

Aziz

Majid

Ismail

2014

Journal of Applied Mathematics

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This paper considers the numerical solution of delay differential equations for solving the problem of small and vanishing lag using multistep block method. This problem arises when the size of a delay value is smaller than the step size,x-τ<h, and the delay time may even vanish whenτ→0in a current step. The proposed approach that is based on interpolation of Newton divided difference has been implemented by adapting this problem to the multistep block method. In order to achieve the required accuracy, this approach considered the appropriate degree of interpolation polynomial in approximating the solution of delay term. The developed code for solving small and vanishing lag is done using C program and we called it as DDEB5. TheP-stability andQ-stability of this method are also studied. Numerical results are presented and compared to the existing method in order to illustrate the efficiency of the proposed method.

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Variable-step variable-order 3-stage Hermite–Birkhoff–Obrechkoff DDE solver of order 4 to 14

Cited by 2 publications

References 9 publications

Multistep block method for solving vanishing delay differential equations

Multistep block method for solving vanishing delay differential equations

Solving Delay Differential Equations of Small and Vanishing Lag Using Multistep Block Method

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