Extended double-stride L-stable methods for the numerical solution of ODEs

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

doi:10.1016/0898-1221(95)00187-5

Cited by 10 publications

(3 citation statements)

References 5 publications

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“…Special classes of MIRK methods, where the stages are evaluated in equidistant points with integer values 0, 1,... ,s -1 have been studied by the present authors [22]; they have shown that MIRK methods belonging to this subclass are completely equivalent to the previously introduced extended one-step methods [20,13,6,7]. In [10] it has been shown that a one-parameter family of double-stride L-stable methods of fourth-order, obtained by the coupling of three linear multistep methods [8] can also be included within the framework of MIRK methods. P-stable methods for second-order ODEs of the form y"= f(t, y) are constructed either by considering so-called symmetric hybrid methods [3,4,9,[17][18][19] or by using IRKN methods [12].…”

Section: Introductionmentioning

confidence: 83%

On the generation of mono-implicit Runge-Kutta-Nyström methods by mono-implicit Runge-Kutta methods

Meyer¹,

Berghe²,

Hecke³

et al. 1997

Journal of Computational and Applied Mathematics

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Mono-implicit Runge-Kutta methods can be used to generate implicit Runge-Kutta-Nystr6m (IRKN) methods for the numerical solution of systems of second-order differential equations. The paper is concerned with the investigation of the conditions to be fulfilled by the mono-implicit Runge-Kutta (MIRK) method in order to generate a mono-implicit Runge-Kutta-Nystr6m method (MIRKN) that is P-stable. One of the main theoretical results is the property that MIRK methods (in standard form) cannot generate MIRKN methods (in standard form) of order greater than 4. Many examples of MIRKN methods generated by MIRK methods are presented.

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Section: Introductionmentioning

confidence: 83%

On the generation of mono-implicit Runge-Kutta-Nyström methods by mono-implicit Runge-Kutta methods

Meyer¹,

Berghe²,

Hecke³

et al. 1997

Journal of Computational and Applied Mathematics

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“…[3] presented the method of Lie group of transformations, which makes convection-diffusion equation invariant. The one-parameter  -Lie group point of transformations are given by (10) The infinitesimal generator for ( 10) is given by (11) and the second prolongation of the infinitesimal generator ( 11) is given by…”

Section: Lie Group Transformation Methodsmentioning

confidence: 99%

Numerical Solution of Convection-Diffusion Equation by Chebyshev Spectral Method via Lie Group Method

Assabaai¹

2021

Yanbu Journal of Engineering and Science

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The numerical solution of convection-diffusion equation is presented by using Chebyshev spectral method based on El-Gendi method via Lie group analysis. Firstly, we apply Lie symmetry group analysis for the convection-diffusion equation. This method yields convection-diffusion equation to a system of ordinary differential equations (ODEs). Secondly, this system is solved numerically by using Chebyshev spectral method. The numerical results obtained by this way are compared with the exact solution.

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“…The CN scheme employs a classical trapezoidal formula for time integration and second-order central difference formulas for the discretization of asset derivatives. Chawla et al [10] presented high-accuracy finite-difference methods for the Black-Scholes equation in which they employed the fourthorder L-stable time integration schemes (LSIMP) developed by Chawla et al [11] and the well-known Numerov method for discretization in terms of the asset direction. Company et al [12] constructed a finite difference scheme and the numerical analysis of its solution for a nonlinear Black-Scholes partial differential equation, modeling stock option prices in the realistic case in which transaction costs arising in the hedging of portfolios are taken into account.…”

Section: Introductionmentioning

confidence: 99%

B-spline Collocation Approach to the Solution of Options Pricing Model

Rashidinia¹,

Jamalzadeh²,

Mohebianfar³

2014

JCSCM

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In this paper, we construct a numerical method to the solution of the Black-Scholes partial differential equation modeling the European option pricing problem with regard to a single asset. W e use an explicit spline-difference scheme which is based on using a finite difference approximation for the temporal derivative and a cubic B-spline collocation for spatial derivatives. The derived method leads to a tri-diagonal linear system. The stability of this method has been discussed and shown to be unconditionally stable. The computational performance of the proposed scheme is compared with those obtained by using a scheme based on the radial basis function.

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Extended double-stride L-stable methods for the numerical solution of ODEs

Cited by 10 publications

References 5 publications

On the generation of mono-implicit Runge-Kutta-Nyström methods by mono-implicit Runge-Kutta methods

On the generation of mono-implicit Runge-Kutta-Nyström methods by mono-implicit Runge-Kutta methods

Numerical Solution of Convection-Diffusion Equation by Chebyshev Spectral Method via Lie Group Method

B-spline Collocation Approach to the Solution of Options Pricing Model

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