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41.
Semi-Lagrangian (SL) methods have been very popular in the Vlasov simulation community , , , , , , and . In this paper, we propose a new Strang split SL discontinuous Galerkin (DG) method for solving the Vlasov equation. Specifically, we apply the Strang splitting for the Vlasov equation [6], as a way to decouple the nonlinear Vlasov system into a sequence of 1-D advection equations, each of which has an advection velocity that only depends on coordinates that are transverse to the direction of propagation. To evolve the decoupled linear equations, we propose to couple the SL framework with the semi-discrete DG formulation. The proposed SL DG method is free of time step restriction compared with the Runge–Kutta DG method, which is known to suffer from numerical time step limitation with relatively small CFL numbers according to linear stability analysis. We apply the recently developed positivity preserving (PP) limiter [37], which is a low-cost black box procedure, to our scheme to ensure the positivity of the unknown probability density function without affecting the high order accuracy of the base SL DG scheme. We analyze the stability and accuracy properties of the SL DG scheme by establishing its connection with the direct and weak formulations of the characteristics/Lagrangian Galerkin method [23]. The quality of the proposed method is demonstrated via basic test problems, such as linear advection and rigid body rotation, and via classical plasma problems, such as Landau damping and the two stream instability. 相似文献
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Chein‐Shan Liu 《Numerical Methods for Partial Differential Equations》2007,23(5):1083-1109
We consider an inverse problem for estimating the two coefficient functions c and k in a parabolic type partial differential equation c(u)ut = ?[k(u)ux]/?x with the aid of the measurements of u at two different times. The first‐ and second‐order one‐step group preserving schemes are developed. Solving the resultant algebraic equations with a closed‐form, we can estimate the unknown temperature‐dependent thermal conductivity and heat capacity. The new methods possess threefold advantages: they do not require any a priori information on the functional forms of thermal conductivity and heat capacity; no initial guesses are required; and no iterations are required. Numerical examples are examined to show that the new approaches have high accuracy and efficiency, even there are rare measured data. When the measured temperatures are polluted by uniform or normal random noise, the estimated results are also good. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 相似文献
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Zeng FanPing 《东北数学》1997,(2)
TheMeasure┐PreservingShiftontheCantorSet*)ZengFanPing**)(曾凡平)(DepartmentofMathematics,NanjingUniversity,Nanjing,210093)Abstra... 相似文献
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Stability,periodicity, and symmetries of certain second‐order fractional difference equation with quadratic terms via KAM theory
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Mirela Garić‐Demirović M. Nurkanović Z. Nurkanović 《Mathematical Methods in the Applied Sciences》2017,40(1):306-318
By using the Kolmogorov–Arnold–Moser theory, we investigate the stability of the equilibrium solution of the difference equation where A ,B ,D > 0,u ?1,u 0>0. We also use the symmetries to find effectively the periodic solutions with feasible periods. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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Let X and Y be superreflexive complex Banach spaces and let B(X) and B(Y) be the Banach algebras of all bounded linear operators on X and Y, respectively. If a bijective linear map Φ:B(X)→B(Y) almost preserves the spectra, then it is almost multiplicative or anti-multiplicative. Furthermore, in the case where X=Y is a separable complex Hilbert space, such a map is a small perturbation of an automorphism or an anti-automorphism. 相似文献