Numerical Simulation of the Lorenz-Type Chaotic System Using Barycentric Lagrange Interpolation Collocation Method

Li, Junmei; Wang, Yulan; Zhang, Wei

doi:10.1155/2019/1030318

Cited by 6 publications

(4 citation statements)

References 26 publications

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“…We execute the following iterative methods to solve IVPs and the system of IVPs [19], [20]. All numerical computations were performed using a Mat Lab 2011Rb laptop (Processor Intel® Core™ i3-3310m CPU@2.4GHz with 64-bit operating system) on Windows 8.…”

Section: Numerical Outcomesmentioning

confidence: 99%

Stable Computer Method for Solving Initial Value Problems with Engineering Applications

Shams¹,

Kausar²,

Ozbilge³

et al. 2023

Computer Systems Science and Engineering

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Engineering and applied mathematics disciplines that involve differential equations in general, and initial value problems in particular, include classical mechanics, thermodynamics, electromagnetism, and the general theory of relativity. A reliable, stable, efficient, and consistent numerical scheme is frequently required for modelling and simulation of a wide range of real-world problems using differential equations. In this study, the tangent slope is assumed to be the contra-harmonic mean, in which the arithmetic mean is used as a correction instead of Euler's method to improve the efficiency of the improved Euler's technique for solving ordinary differential equations with initial conditions. The stability, consistency, and efficiency of the system were evaluated, and the conclusions were supported by the presentation of numerical test applications in engineering. According to the stability analysis, the proposed method has a wider stability region than other well-known methods that are currently used in the literature for solving initial-value problems. To validate the rate convergence of the numerical technique, a few initial value problems of both scalar and vector valued types were examined. The proposed method, modified Euler explicit method, and other methods known in the literature have all been used to calculate the absolute maximum error, absolute error at the last grid point of the integration interval under consideration, and computational time in seconds to test the performance. The Lorentz system was used as an example to illustrate the validity of the solution provided by the newly developed method. The method is determined to be more reliable than the commonly existing methods with the same order of convergence, as mentioned in the literature for numerical calculations and visualization of the results produced by all the methods discussed, Mat Lab-R2011b has been used.

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Section: Numerical Outcomesmentioning

confidence: 99%

Stable Computer Method for Solving Initial Value Problems with Engineering Applications

Shams¹,

Kausar²,

Ozbilge³

et al. 2023

Computer Systems Science and Engineering

View full text Add to dashboard Cite

show abstract

“…Since then, many researchers have been studying the effects parameters and initial conditions have on chaos attractor. Among them includes finding analytical solutions by authors such as [2][3][4][5][6][7][8] and numerical solutions in works of [9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis on chaos attractors using a backward difference formulation

Rasedee¹,

Sathar²,

Najib³

et al. 2022

Math. Model. Comput.

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The chaos attractor is a system of ordinary differential equations which is known for having chaotic solutions for certain parameter values and an initial condition. Research conducted in the current work establishes a backward difference algorithm to study these chaos attractors. Different types of chaos mapping, namely the Lorenz chaos, 'sandwich' chaos and 'horseshoe' chaos will be analyzed. Compared to other numerical methods, the proposed backward difference algorithm will show to be an efficient tool for analyzing solutions for the chaos attractors.

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“…In engineering, a fast estimation of the periodic property of a nonlinear oscillator is much needed. As an exact solution might be too complex to be used for a practical application, many analytical and numerical methods have been used in open literature, for example, the homotopy perturbation method, [1][2][3][4] the barycentric interpolation collocation method, [5][6] the variational iteration method, [7][8][9][10][11] and the reproducing kernel method [12][13][14][15][16] which are still under development and many modifications were proposed to improve the accuracy.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of a class of space fractional nonlinear vibration equations with periodic boundary conditions by the Fourier spectral method

Zhu¹,

Han

Liu

et al. 2021

Journal of Low Frequency Noise, Vibration and Active Control

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Nonlinear vibration arises everywhere in engineering. So far there is no method to track the exact trajectory of a space fractional nonlinear oscillator; therefore, a sophisticated numerical method is much needed to elucidate its basic properties. For this purpose, a numerical method that combines the Fourier spectral method with the Runge–Kutta method is proposed. Its accuracy and efficiency have been demonstrated numerically. This approach has full physical understanding and numerical access; thus, it can be used to solve many types of nonlinear space fractional partial differential equations with periodic boundary conditions.

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Numerical Simulation of the Lorenz-Type Chaotic System Using Barycentric Lagrange Interpolation Collocation Method

Cited by 6 publications

References 26 publications

Stable Computer Method for Solving Initial Value Problems with Engineering Applications

Stable Computer Method for Solving Initial Value Problems with Engineering Applications

Numerical analysis on chaos attractors using a backward difference formulation

Numerical solution of a class of space fractional nonlinear vibration equations with periodic boundary conditions by the Fourier spectral method

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