The Experts below are selected from a list of 1560 Experts worldwide ranked by ideXlab platform
Yuri E Litvinenko - One of the best experts on this subject based on the ideXlab platform.
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the diffusion approximation vs the telegraph equation for modeling solar energetic particle transport with adiabatic focusing i isotropic pitch angle scattering
arXiv: Space Physics, 2014Co-Authors: Frederic Effenberger, Yuri E LitvinenkoAbstract:The diffusion approximation to the Fokker-Planck equation is commonly used to model the transport of solar energetic particles in interplanetary space. In this study, we present exact analytical predictions of a higher order telegraph approximation for particle transport and compare them with the corresponding predictions of the diffusion approximation and numerical solutions of the full Fokker-Planck equation. We specifically investigate the role of the adiabatic focusing effect of a spatially varying magnetic field on an evolving particle distribution. Comparison of the analytical and numerical results shows that the telegraph approximation reproduces the particle intensity profiles much more accurately than does the diffusion approximation, especially when the focusing is strong. However, the telegraph approximation appears to offer no significant advantage over the diffusion approximation for calculating the particle anisotropy. The telegraph approximation can be a useful tool for describing both diffusive and wavelike aspects of the cosmic-ray transport.
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the diffusion approximation versus the telegraph equation for modeling solar energetic particle transport with adiabatic focusing i isotropic pitch angle scattering
The Astrophysical Journal, 2014Co-Authors: Frederic Effenberger, Yuri E LitvinenkoAbstract:The diffusion approximation to the Fokker-Planck equation is commonly used to model the transport of solar energetic particles in interplanetary space. In this study, we present exact analytical predictions of a higher order telegraph approximation for particle transport and compare them with the corresponding predictions of the diffusion approximation and numerical solutions of the full Fokker-Planck equation. We specifically investigate the role of the adiabatic focusing effect of a spatially varying magnetic field on an evolving particle distribution. Comparison of the analytical and numerical results shows that the telegraph approximation reproduces the particle intensity profiles much more accurately than does the diffusion approximation, especially when the focusing is strong. However, the telegraph approximation appears to offer no significant advantage over the diffusion approximation for calculating the particle anisotropy. The telegraph approximation can be a useful tool for describing both diffusive and wave-like aspects of the cosmic-ray transport.
Abdon Atangana - One of the best experts on this subject based on the ideXlab platform.
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on the stability and convergence of the time fractional variable order telegraph equation
Journal of Computational Physics, 2015Co-Authors: Abdon AtanganaAbstract:In this work, we have generalized the time-fractional telegraph equation using the concept of derivative of fractional variable order. The generalized equation is called time-fractional variable order telegraph equation. This new equation was solved numerically via the Crank-Nicholson scheme. Stability and convergence of the numerical solution were presented in details. Numerical simulations of the approximate solution of the time-fractional variable order telegraph equation were presented for different values of the grid point.
Frederic Effenberger - One of the best experts on this subject based on the ideXlab platform.
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the diffusion approximation vs the telegraph equation for modeling solar energetic particle transport with adiabatic focusing i isotropic pitch angle scattering
arXiv: Space Physics, 2014Co-Authors: Frederic Effenberger, Yuri E LitvinenkoAbstract:The diffusion approximation to the Fokker-Planck equation is commonly used to model the transport of solar energetic particles in interplanetary space. In this study, we present exact analytical predictions of a higher order telegraph approximation for particle transport and compare them with the corresponding predictions of the diffusion approximation and numerical solutions of the full Fokker-Planck equation. We specifically investigate the role of the adiabatic focusing effect of a spatially varying magnetic field on an evolving particle distribution. Comparison of the analytical and numerical results shows that the telegraph approximation reproduces the particle intensity profiles much more accurately than does the diffusion approximation, especially when the focusing is strong. However, the telegraph approximation appears to offer no significant advantage over the diffusion approximation for calculating the particle anisotropy. The telegraph approximation can be a useful tool for describing both diffusive and wavelike aspects of the cosmic-ray transport.
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the diffusion approximation versus the telegraph equation for modeling solar energetic particle transport with adiabatic focusing i isotropic pitch angle scattering
The Astrophysical Journal, 2014Co-Authors: Frederic Effenberger, Yuri E LitvinenkoAbstract:The diffusion approximation to the Fokker-Planck equation is commonly used to model the transport of solar energetic particles in interplanetary space. In this study, we present exact analytical predictions of a higher order telegraph approximation for particle transport and compare them with the corresponding predictions of the diffusion approximation and numerical solutions of the full Fokker-Planck equation. We specifically investigate the role of the adiabatic focusing effect of a spatially varying magnetic field on an evolving particle distribution. Comparison of the analytical and numerical results shows that the telegraph approximation reproduces the particle intensity profiles much more accurately than does the diffusion approximation, especially when the focusing is strong. However, the telegraph approximation appears to offer no significant advantage over the diffusion approximation for calculating the particle anisotropy. The telegraph approximation can be a useful tool for describing both diffusive and wave-like aspects of the cosmic-ray transport.
Surabhi Tiwari - One of the best experts on this subject based on the ideXlab platform.
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Numerical simulation of second-order hyperbolic telegraph type equations with variable coefficients
Computer Physics Communications, 2015Co-Authors: Sapna Pandit, Manoj Kumar, Surabhi TiwariAbstract:Abstract In this article, the authors proposed a numerical scheme based on Crank–Nicolson finite difference scheme and Haar wavelets to find numerical solutions of different types of second order hyperbolic telegraph equations (i.e. telegraph equation with constant coefficients, with variable coefficients, and singular telegraph equation). This work is an extension of the scheme by Jiwari (2012) for hyperbolic equations. The use of Haar basis function is made with multiresolution analysis to get the fast and accurate results on collocation points. The convergence of the proposed scheme is proved by doing its error analysis. Four test examples are considered to demonstrate the accuracy and efficiency of the scheme. The scheme is easy and very suitable for computer implementation and provides numerical solutions close to the exact solutions and available in the literature.
T S Jang - One of the best experts on this subject based on the ideXlab platform.
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a new solution procedure for the nonlinear telegraph equation
Communications in Nonlinear Science and Numerical Simulation, 2015Co-Authors: T S JangAbstract:Abstract This paper involves a theoretical but fundamental question in the numerical computation of partial differential equations. Is it possible to construct the solution for a nonlinear telegraph equation (or a nonlinear damped wave equation) by using a hyperbolic linear solution of Klein–Gordon equation? To answer the question, firstly, an analytic solution of the linear Klein–Gordon equation is introduced here. Through the introduction, we show how the original nonlinear telegraph equation can be transformed into an equivalent nonlinear system of two integral equations of the second kind. Here, the singularities of the system's kernels are asymptotically shown to be just removable. Then, the above question may be answered by applying Banach fixed point theorem to the two (coupled) integral equations and thus showing how to construct nonlinear iterative solutions of the telegraph equation. This results in a new (functional) iterative procedure for the constructing of the (numerical) solutions of a general nonlinear telegraph equation.
