Results 1 to 10 of about 15,682 (128)
Acta Numerica, 2010 In this paper we consider the construction, analysis, implementation and application of exponential integrators. The focus will be on two types of stiff problems. The first one is characterized by a Jacobian that possesses eigenvalues with large negative real parts.
Hochbruck, Marlis, Ostermann, Alexander
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Integration of modules – II: Exponentials [PDF]
Transactions of the American Mathematical Society, 2021 Accepted by Transactions of the AMS. This paper is split off the earlier versions (1, 2 and 3) of arXiv:1708.06620. Some of the statements in these versions of arXiv:1708.06620 contain mistakes corrected here. Version 2 of this paper: close to the accepted version by the journal, minor improvements, compared to Version ...
Dmitriy Rumynin, Matthew Westaway
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Energy Minimization Scheme for Split Potential Systems Using Exponential Variational Integrators
Applied Mechanics, 2021 In previous works we developed a methodology of deriving variational integrators to provide numerical solutions of systems having oscillatory behavior. These schemes use exponential functions to approximate the intermediate configurations and velocities,
Odysseas Kosmas
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LeXInt: Package for exponential integrators employing Leja interpolation
SoftwareX, 2023 We present a publicly available software for exponential integrators that computes the φl(z)functions using polynomial interpolation. The interpolation method at Leja points have recently been shown to be competitive with the traditionally-used Krylov ...
Pranab J. Deka +2 more
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Geometric exponential integrators [PDF]
Journal of Computational Physics, 2019 18 pages, 11 ...
Xuefeng Shen, Melvin Leok
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Why Improving the Accuracy of Exponential Integrators Can Decrease Their Computational Cost?
Mathematics, 2021 In previous papers, a technique has been suggested to avoid order reduction when integrating initial boundary value problems with several kinds of exponential methods.
Begoña Cano, Nuria Reguera
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Solving the nonlinear Schrödinger equation using exponential integrators [PDF]
Modeling, Identification and Control, 2006 Using the notion of integrating factors, Lawson developed a class of numerical methods for solving stiff systems of ordinary differential equations. However, the performance of these "Generalized Runge - Kutta processes" was demonstrably poorer when ...
Håvard Berland +2 more
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Volume-Preserving Exponential Integrators [PDF]
, 2021 As is known that various dynamical systems including all Hamiltonian systems preserve volume in phase space. This qualitative geometrical property of the analytical solution should be respected in the sense of Geometric Integration. This paper analyses the volume-preserving property of exponential integrators in different vector fields.
Wang, Bin, Wu, Xinyuan
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Complexity, 2021 This paper presents the design, simulation, and experimental verification of the fractional-order multiscroll Lü chaotic system. We base them on op-amp-based approximations of fractional-order integrators and saturated series of nonlinear functions.
Jesus M. Munoz-Pacheco +6 more
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Fractal and Fractional, 2022 In this paper, a family of high-order linearly implicit exponential integrators conservative schemes is constructed for solving the multi-dimensional nonlinear fractional Schrödinger equation.
Yayun Fu +3 more
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