The Experts below are selected from a list of 64353 Experts worldwide ranked by ideXlab platform
Chengjian Zhang - One of the best experts on this subject based on the ideXlab platform.
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a conservative Difference Scheme for solving the strongly coupled nonlinear fractional schrodinger equations
Communications in Nonlinear Science and Numerical Simulation, 2016Co-Authors: Chengjian ZhangAbstract:This paper focuses on numerically solving the strongly coupled nonlinear space fractional Schrodinger equations. First, the laws of conservation of mass and energy are given. Then, an implicit Difference Scheme is proposed, under the assumption that the analytical solution decays to zero when the space variable x tends to infinity. We show that the Scheme conserves the mass and energy and is unconditionally stable with respect to the initial values. Moreover, the solvability, boundedness and convergence in the maximum norm are established. To avoid solving nonlinear systems, a linear Difference Scheme with two identities is proposed. Several numerical experiments are provided to confirm the theoretical results.
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a linear finite Difference Scheme for generalized time fractional burgers equation
Applied Mathematical Modelling, 2016Co-Authors: Dongfang Li, Chengjian ZhangAbstract:Abstract This paper is concerned with the numerical solutions of the generalized time fractional burgers equation. We propose a linear implicit finite Difference Scheme for solving the equation. Iterative methods become dispensable. As a result, the computational cost can be significantly reduced compare to the usual implicit finite Difference Schemes. Meanwhile, the finite Difference method is proved to be unconditional globally stable and convergent. Numerical examples are shown to demonstrate the accuracy and stability of the method.
Wei Yang - One of the best experts on this subject based on the ideXlab platform.
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a linearly implicit conservative Difference Scheme for the space fractional coupled nonlinear schrodinger equations
Journal of Computational Physics, 2014Co-Authors: Dongling Wang, Aiguo Xiao, Wei YangAbstract:Abstract In this paper, a linearly implicit conservative Difference Scheme for the coupled nonlinear Schrodinger equations with space fractional derivative is proposed. This Scheme conserves the mass and energy in the discrete level and only needs to solve a linear system at each step. The existence and uniqueness of the Difference solution are proved. The stability and convergence of the Scheme are discussed, and it is shown to be convergent of order O ( τ 2 + h 2 ) in the discrete l 2 norm with the time step τ and mesh size h . When the fractional order is two, all those results are in accord with the Difference Scheme proposed for the classical non-fractional coupled nonlinear Schrodinger equations. Some numerical examples are also reported.
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crank nicolson Difference Scheme for the coupled nonlinear schrodinger equations with the riesz space fractional derivative
Journal of Computational Physics, 2013Co-Authors: Dongling Wang, Aiguo Xiao, Wei YangAbstract:In this paper, the Crank-Nicolson (CN) Difference Scheme for the coupled nonlinear Schrodinger equations with the Riesz space fractional derivative is studied. The existence of this Difference solution is proved by the Brouwer fixed point theorem. The stability and convergence of the CN Scheme are discussed in the L"2 norm. When the fractional order is two, all those results are in accord with the Difference Scheme developed for the classical non-fractional coupled nonlinear Schrodinger equations. Some numerical examples are also presented.
Dongling Wang - One of the best experts on this subject based on the ideXlab platform.
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a linearly implicit conservative Difference Scheme for the space fractional coupled nonlinear schrodinger equations
Journal of Computational Physics, 2014Co-Authors: Dongling Wang, Aiguo Xiao, Wei YangAbstract:Abstract In this paper, a linearly implicit conservative Difference Scheme for the coupled nonlinear Schrodinger equations with space fractional derivative is proposed. This Scheme conserves the mass and energy in the discrete level and only needs to solve a linear system at each step. The existence and uniqueness of the Difference solution are proved. The stability and convergence of the Scheme are discussed, and it is shown to be convergent of order O ( τ 2 + h 2 ) in the discrete l 2 norm with the time step τ and mesh size h . When the fractional order is two, all those results are in accord with the Difference Scheme proposed for the classical non-fractional coupled nonlinear Schrodinger equations. Some numerical examples are also reported.
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crank nicolson Difference Scheme for the coupled nonlinear schrodinger equations with the riesz space fractional derivative
Journal of Computational Physics, 2013Co-Authors: Dongling Wang, Aiguo Xiao, Wei YangAbstract:In this paper, the Crank-Nicolson (CN) Difference Scheme for the coupled nonlinear Schrodinger equations with the Riesz space fractional derivative is studied. The existence of this Difference solution is proved by the Brouwer fixed point theorem. The stability and convergence of the CN Scheme are discussed in the L"2 norm. When the fractional order is two, all those results are in accord with the Difference Scheme developed for the classical non-fractional coupled nonlinear Schrodinger equations. Some numerical examples are also presented.
Chengming Huang - One of the best experts on this subject based on the ideXlab platform.
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an implicit midpoint Difference Scheme for the fractional ginzburg landau equation
Journal of Computational Physics, 2016Co-Authors: Pengde Wang, Chengming HuangAbstract:This paper proposes and analyzes an efficient Difference Scheme for the nonlinear complex Ginzburg-Landau equation involving fractional Laplacian. The Scheme is based on the implicit midpoint rule for the temporal discretization and a weighted and shifted Grunwald Difference operator for the spatial fractional Laplacian. By virtue of a careful analysis of the Difference operator, some useful inequalities with respect to suitable fractional Sobolev norms are established. Then the numerical solution is shown to be bounded, and convergent in the l h 2 norm with the optimal order O ( ? 2 + h 2 ) with time step ? and mesh size h. The a priori bound as well as the convergence order holds unconditionally, in the sense that no restriction on the time step ? in terms of the mesh size h needs to be assumed. Numerical tests are performed to validate the theoretical results and effectiveness of the Scheme.
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an energy conservative Difference Scheme for the nonlinear fractional schrodinger equations
Journal of Computational Physics, 2015Co-Authors: Pengde Wang, Chengming HuangAbstract:Abstract In this paper, an energy conservative Crank–Nicolson Difference Scheme for nonlinear Riesz space-fractional Schrodinger equations is studied. We give a rigorous analysis of the conservation properties, including mass conservation and energy conservation in the discrete sense. Based on Brouwer fixed point theorem, the existence of the Difference solution is proved. By virtue of the energy method, the Difference solution is shown to be unique and convergent at the order of O ( τ 2 + h 2 ) in the l 2 -norm with time step τ and mesh size h. Finally a linearized iterative algorithm is presented and numerical experiments are given to confirm the theoretical results.
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a conservative linearized Difference Scheme for the nonlinear fractional schrodinger equation
Numerical Algorithms, 2015Co-Authors: Pengde Wang, Chengming HuangAbstract:In this paper, we propose a conservative linearized Difference Scheme for the nonlinear fractional Schrodinger equation. The Scheme efficiently avoids the time consuming iteration procedure necessary for the nonlinear Scheme and thus is time saving relatively. It is rigorously proved that the Scheme is mass conservative and uniquely solvable. Then employing mathematical induction, we further show that the proposed Scheme is convergent at the order of O(?2 + h2) in the l2 norm with time step ? and mesh size h. Moreover, an extension to coupled nonlinear fractional Schrodinger systems is presented. Finally, numerical tests are carried out to corroborate the theoretical results and investigate the impact of the fractional order ? on the collision of two solitons.
R Du - One of the best experts on this subject based on the ideXlab platform.
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a compact Difference Scheme for the fractional diffusion wave equation
Applied Mathematical Modelling, 2010Co-Authors: R DuAbstract:Abstract This article is devoted to the study of high order Difference methods for the fractional diffusion-wave equation. The time fractional derivatives are described in the Caputo’s sense. A compact Difference Scheme is presented and analyzed. It is shown that the Difference Scheme is unconditionally convergent and stable in L ∞ -norm. The convergence order is O ( τ 3 - α + h 4 ) . Two numerical examples are also given to demonstrate the theoretical results.
