On the numerical solution of stiff systems

Güzel, Nuran; Bayram, Mustafa

doi:10.1016/j.amc.2004.11.035

Cited by 28 publications

(20 citation statements)

References 5 publications

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“…This problem was as well solved by Guzel and Bayram [6] who applied the power series method. Hojjati et al [8] solved (3.4) with the aid of a predictorcorrector method, based on backward differentiation.…”

Section: ü Lepikmentioning

confidence: 99%

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Haar Wavelet Method for Solving Stiff Differential Equations

Lepik

2009

Mathematical Modelling and Analysis

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Section: ü Lepikmentioning

confidence: 99%

“…We would like to turn attention also to the paper [4] by Enright et al in which different numerical methods have been tested for solving 25 systems of stiff equations. From the recent literature we refer here [1,5,6,8,12,16,18].…”

Section: Introductionmentioning

confidence: 99%

Haar Wavelet Method for Solving Stiff Differential Equations

Lepik

2009

Mathematical Modelling and Analysis

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“…But using spectral method based on new rational basis functions, we show the accuracy and superiority of our new basis functions rather than other basis functions such as polynomials in global interval. Experiment 3.Consider the following system of differential equations [33], our new basis functions rather than other basis functions such as polynomials in global interval.…”

Section: The Test Experimentsmentioning

confidence: 99%

Rational Laguerre Functions And Their Applications

Aminataei¹,

Asl²,

Kalatehbojdi³

2015

J. Math. Computer Sci.

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In this work, we introduce a new class of rational basis functions defined on [ , ) ab and based on mapping the Laguerre polynomials on the bounded domain [ , ) ab . By using these rational functions as basic functions, we implement spectral methods for numerical solutions of operator equations. Also the quadrature formulae and operational matrices (derivative, integral and product) with respect to these basis functions are obtained. We show that using quadrature formulae based on rational Laguerre functions give us very good results for numerical integration of rational functions and also implementing spectral methods based on these basis functions for solving stiff systems of ordinary differential equationsgive us suitable results. The details of the convergence rates of these basis functions for the solutions of operator equations are carried out, both theoretically and computationally and the error analysis is presented in   2 [ , ) L a b space norm.

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“…Interested reader can read, for instance, [12] in conjunction with the present paper to see furhter applications of this method to some other nonlinear fractional systems. One can employ some other numerical methods such as the ones presented at [9]- [11] as well as Milne's and Adomian decomposition methods. Now, firstly let us write the incommensurate fractional order Shimizu-Morioka dynamical system once again.…”

Section: Numerical Solutionmentioning

confidence: 99%

Stability, Synchronization Control and Numerical Solution of Fractional Shimizu–Morioka Dynamical System

Akinlar¹,

Seçer²,

Bayram³

2014

Appl. Math. Inf. Sci.

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Abstract:In this paper we concern with asymptotic stability, synchronization control and numerical solution of incommensurate order fractional Shimizu-Morioka dynamical system. Firstly we prove the existence and uniqueness of the solutions via a new theorem. After finding steady-state points, we obtain necessary and sufficient conditions for the asymptotic stability of the Shimizu-Morioka system. We also study the synchronization control where we employ master-slave synchronization scheme. Finally, employing AdamsBashforth-Moulton's technique we solve the Shimizu-Morioka system numerically. To the best of our knowledge, there exist not any study about analysis of chaotic dynamics of fractional Shimizu-Morioka system in the literature. In this sense the present paper is going to be a totally new contribution and highly useful research for synthesis of a nonlinear system of fractional equations.

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On the numerical solution of stiff systems

Cited by 28 publications

References 5 publications

Haar Wavelet Method for Solving Stiff Differential Equations

Haar Wavelet Method for Solving Stiff Differential Equations

Rational Laguerre Functions And Their Applications

Stability, Synchronization Control and Numerical Solution of Fractional Shimizu–Morioka Dynamical System

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