The efficiency of second derivative multistep methods for the numerical integration of stiff systems

Yakubu, D. G.; Markuš, Š.

doi:10.1016/j.jnnms.2016.02.002

Cited by 9 publications

(6 citation statements)

References 20 publications

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“…It results from the decaying of some of the solution components being more rapidly than other components as they contain the term e -λt , λ > 0. However, many numerical and analytical techniques have been employed recently for solving stiff systems of ordinary differential equations including the homotopy perturbation method [3], the block method [4], the multistep method [5], and the variational iteration method [6]. Ex-amples of another mathematical models and effective numerical solutions can be found in [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Construction of fractional power series solutions to fractional stiff system using residual functions algorithm

et al. 2019

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A powerful analytical approach, namely the fractional residual power series method (FRPS), is applied successfully in this work to solving a class of fractional stiff systems. The methodology of the FRPS method gets a Maclaurin expansion of the solution in rapidly convergent form and apparent sequences based on the Caputo sense without any restriction hypothesis. This approach is tested on a fractional stiff system with nonlinearity ranging. Meanwhile, stability and convergence study are presented in the domain of interest. Illustrative examples justify that the proposed method is analytically effective and convenient, and it can be implemented in a large number of engineering problems. A numerical comparison for the experimental data with another well-known method, the reproducing kernel method, is given. The graphical consequences illuminate the simplicity and reliability of the FRPS method in the determination of the RPS solutions consistently.

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Section: Introductionmentioning

confidence: 99%

Construction of fractional power series solutions to fractional stiff system using residual functions algorithm

et al. 2019

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“…We compared our results with the Second Derivative Multistep Method of order 10 (SDMM 10 ) by Yakubu and Marcus [8]. Our methods gave better approximation despite the low order as shown in Table III…”

Section: Numerical Examplesmentioning

confidence: 96%

On nonlinear methods for stiff and singular first order initial value problems

Adesanya¹,

Pantuvo²,

Umar³

2018

nade

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This paper considers development of nonlinear method by interpolation and collocation of inverse polynomial approximate solution to give systems of equations, solving for the unknown parameters and substituting the results into the approximate solution gives a continuous method. We evaluated the continuous method at different grid points to give discrete methods which are implemented without developing separate predictors. The method is convergent and A-stable, numerical examples show that the method is good for stiff and singular problems.

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“…During studying and modeling many basic physical phenomena, such as chemical kinematics, aerodynamics, electrical circuits, ballistics, control models, and missile guidance, a type of differential equations appears that is difficult to solve through traditional numerical procedures, called differential stiffness system, which was first highlighted in the work of Curtiss and Hirschfelder [1][2][3][4][5][6]. Mathematical stiffness models reflect the different growth rates and various dynamic processes of the considered physical systems.…”

Section: Introductionmentioning

confidence: 99%

Attractive Multistep Reproducing Kernel Approach for Solving Stiffness Differential Systems of Ordinary Differential Equations and SomeError Analysis

Abu-Gdairi¹,

Hasan²,

Al‐Omari³

et al. 2022

Computer Modeling in Engineering &Amp; Sciences

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In this paper, an efficient multi-step scheme is presented based on reproducing kernel Hilbert space (RKHS) theory for solving ordinary stiff differential systems. The solution methodology depends on reproducing kernel functions to obtain analytic solutions in a uniform form for a rapidly convergent series in the posed Sobolev space. Using the Gram-Schmidt orthogonality process, complete orthogonal essential functions are obtained in a compact field to encompass Fourier series expansion with the help of kernel properties reproduction. Consequently, by applying the standard RKHS method to each subinterval, approximate solutions that converge uniformly to the exact solutions are obtained. For this purpose, several numerical examples are tested to show proposed algorithm's superiority, simplicity, and efficiency. The gained results indicate that the multi-step RKHS method is suitable for solving linear and nonlinear stiffness systems over an extensive duration and giving highly accurate outcomes.

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The efficiency of second derivative multistep methods for the numerical integration of stiff systems

Cited by 9 publications

References 20 publications

Construction of fractional power series solutions to fractional stiff system using residual functions algorithm

Construction of fractional power series solutions to fractional stiff system using residual functions algorithm

On nonlinear methods for stiff and singular first order initial value problems

Attractive Multistep Reproducing Kernel Approach for Solving Stiffness Differential Systems of Ordinary Differential Equations and SomeError Analysis

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