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Block Preconditioning Matrices for the Newton Method to Compute the Dominant λ-Modes Associated with the Neutron Diffusion Equation
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Chaos and Relativistic Energy-Momentum of the Nonlinear Time Fractional Duffing Equation

Department of Mathematics, Faculty of Science, Jiangsu University, Zhenjiang 212013, China
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Math. Comput. Appl. 2019, 24(1), 10; https://doi.org/10.3390/mca24010010
Received: 20 December 2018 / Revised: 9 January 2019 / Accepted: 11 January 2019 / Published: 16 January 2019
This paper studies the nonlinear fractional undamped Duffing equation. The Duffing equation is one of the fundamental equations in engineering. The geographical areas of this model represent chaos, relativistic energy-momentum, electrodynamics, and electromagnetic interactions. These properties have many benefits in different science fields. The equation depicts the energy of a point mass, which is well thought out as a periodically-forced oscillator. We employed twelve different techniques to the nonlinear fractional Duffing equation to find explicit solutions and approximate solutions. The stability of the solutions was also examined to show the ability of our obtained solutions in the application. The main goals here were to apply a novel computational method (modified auxiliary equation method) and compare the novel method with other methods via the solutions that were obtained by each of these methods. View Full-Text
Keywords: chaotic attractor of the Duffing oscillator; fission and fusion phenomena; solitons; nonlinear time fractional Duffing equation; multiple traveling wave methods chaotic attractor of the Duffing oscillator; fission and fusion phenomena; solitons; nonlinear time fractional Duffing equation; multiple traveling wave methods
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Attia, R.A.M.; Lu, D.; M. A. Khater, M. Chaos and Relativistic Energy-Momentum of the Nonlinear Time Fractional Duffing Equation. Math. Comput. Appl. 2019, 24, 10.

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