A class of stabilized extended one-step methods for the numerical solution of ODEs

Al-Zanaidi, M. A.; Al-Sahhar, M.S.

doi:10.1016/0898-1221(95)00048-4

Cited by 19 publications

(8 citation statements)

References 4 publications

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“…We include here a third order time integration scheme based on the extended one-step third order L-stable method for the integration of y 0 ¼ f ðt; yÞ; see Chawla et al [7]. Now, by applying it for the time integration of (2.5) we have…”

Section: A Third Order Time Integration Schemementioning

confidence: 99%

Generalized Trapezoidal Formulas for the Symmetric Heat Equation in Polar Coordinates

Al-Zanaidi

Evans

2002

International Journal of Computer Mathematics

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This paper has two objectives. We first describe one-step time integration schemes for the symmetric heat equation in polar coordinates: u t ¼ nðu rr þ ða=rÞu r Þ based on the generalized trapezoidal formulas (GTF(a)) of Chawla et al. [2]. This includes the case of cylindrical symmetry for a ¼ 1 and of spherical symmetry for a ¼ 2. The obtained GTF(a) time integration schemes are second order in time and unconditionally stable. We then introduce generalized finite Hankel transforms to obtain an analytical solution of the heat equation for all a 1, with Dirichlet and Neumann type boundary conditions. Numerical experiments are provided to compare the accuracy and stability of the obtained GTF(a) time integration schemes with the schemes based on the backward Euler, the classical arithmetic-mean trapezoidal formula and a third order time integration scheme.

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Section: A Third Order Time Integration Schemementioning

confidence: 99%

Generalized Trapezoidal Formulas for the Symmetric Heat Equation in Polar Coordinates

Al-Zanaidi

Evans

2002

International Journal of Computer Mathematics

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“…Several authors have studied the so-called extended one-step methods [1]- [4]. It has been shown by the present authors [5,6] that these methods can also be expressed as special mono-implicit Runge-Kutta methods.…”

Section: Introductionmentioning

confidence: 95%

Extended One‐Step Methods: An Exponential Fitting Approach

Daele

Berghe

2004

Appl Numer Analy & Comput

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Exponentially fitted versions of the extended one‐step methods for first‐order ODEs are constructed following the six‐step flow chart introduced by Ixaru and Vanden Berghe in Exponential fitting, (Mathematics and Its Application 568, Kluwer Academic Publishers, 2004) and their properties are examined. It is shown how formulae for optimal frequencies can be constructed. Some numerical experiments illustrate the use of the developed algorithms. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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“…Chawla et al [14] described fourth order extended one-step methods, which are A-and/or L-stable. Chawla et al [15] derived fifth order extended one-step methods, which are A-and/or L-stable. Chawla et al [16] obtained a one-parameter family of double-stride L-stable methods of fourth order by the coupling of three linear multistep methods.…”

Section: Introductionmentioning

confidence: 99%

Optimal extended one-step schemes of exponential type for stiff initial-value problems

Salama¹,

Bakr²

2004

International Journal of Computer Mathematics

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A class of stabilized extended one-step methods for the numerical solution of ODEs

Cited by 19 publications

References 4 publications

Generalized Trapezoidal Formulas for the Symmetric Heat Equation in Polar Coordinates

Generalized Trapezoidal Formulas for the Symmetric Heat Equation in Polar Coordinates

Extended One‐Step Methods: An Exponential Fitting Approach

Optimal extended one-step schemes of exponential type for stiff initial-value problems

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