The Experts below are selected from a list of 27147 Experts worldwide ranked by ideXlab platform
Chang-ming Chen - One of the best experts on this subject based on the ideXlab platform.
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Numerical Approximation for a variable-order nonlinear reaction–subdiffusion equation
Science & Engineering Faculty, 2013Co-Authors: Chang-ming Chen, Ian Turner, Y. ChenAbstract:Fractional reaction–subdiffusion equations are widely used in recent years to simulate physical phenomena. In this paper, we consider a variable-order nonlinear reaction–subdiffusion equation. A Numerical Approximation method is proposed to solve the equation. Its convergence and stability are analyzed by Fourier analysis. By means of the technique for improving temporal accuracy, we also propose an improved Numerical Approximation. Finally, the effectiveness of the theoretical results is demonstrated by Numerical examples.
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Numerical Approximation for a variable-order nonlinear reaction---subdiffusion equation
Numerical Algorithms, 2012Co-Authors: Chang-ming Chen, Ian Turner, Y. ChenAbstract:Fractional reaction---subdiffusion equations are widely used in recent years to simulate physical phenomena. In this paper, we consider a variable-order nonlinear reaction---subdiffusion equation. A Numerical Approximation method is proposed to solve the equation. Its convergence and stability are analyzed by Fourier analysis. By means of the technique for improving temporal accuracy, we also propose an improved Numerical Approximation. Finally, the effectiveness of the theoretical results is demonstrated by Numerical examples.
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A Numerical Approximation method for solving a three-dimensional space Galilei invariant fractional advection-diffusion equation
Journal of Applied Mathematics and Computing, 2009Co-Authors: Chang-ming ChenAbstract:In this paper, a Numerical Approximation method for solving a three-dimensional space Galilei invariant fractional advection diffusion equation is presented. The convergence and stability of the Numerical Approximation method are discussed by a new technique of Fourier analysis. The solvability of the Numerical Approximation method also is analyzed. Finally, applying Richardson extrapolation technique, a high-accuracy algorithm is structured and the Numerical example demonstrated the theoretical results.
Y. Chen - One of the best experts on this subject based on the ideXlab platform.
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Numerical Approximation for a variable-order nonlinear reaction–subdiffusion equation
Science & Engineering Faculty, 2013Co-Authors: Chang-ming Chen, Ian Turner, Y. ChenAbstract:Fractional reaction–subdiffusion equations are widely used in recent years to simulate physical phenomena. In this paper, we consider a variable-order nonlinear reaction–subdiffusion equation. A Numerical Approximation method is proposed to solve the equation. Its convergence and stability are analyzed by Fourier analysis. By means of the technique for improving temporal accuracy, we also propose an improved Numerical Approximation. Finally, the effectiveness of the theoretical results is demonstrated by Numerical examples.
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Numerical Approximation for a variable-order nonlinear reaction---subdiffusion equation
Numerical Algorithms, 2012Co-Authors: Chang-ming Chen, Ian Turner, Y. ChenAbstract:Fractional reaction---subdiffusion equations are widely used in recent years to simulate physical phenomena. In this paper, we consider a variable-order nonlinear reaction---subdiffusion equation. A Numerical Approximation method is proposed to solve the equation. Its convergence and stability are analyzed by Fourier analysis. By means of the technique for improving temporal accuracy, we also propose an improved Numerical Approximation. Finally, the effectiveness of the theoretical results is demonstrated by Numerical examples.
J. Kaneko - One of the best experts on this subject based on the ideXlab platform.
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A Numerical Approximation method for stochastic differential equations of Ito type
Proceedings of 32nd IEEE Conference on Decision and Control, 1993Co-Authors: J. KanekoAbstract:A higher order scheme is developed for the Numerical Approximation of the solutions to stochastic differential equations of Ito type. The Numerical scheme is of implicit Runge-Kutta (IRK) method which is recognized as appropriate for stiff equations. As the results of error analysis, it is shown that the IRK scheme has 1.5 order accuracy and asymptotic efficiency.
Ian Turner - One of the best experts on this subject based on the ideXlab platform.
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a novel Numerical Approximation for the space fractional advection dispersion equation
Ima Journal of Applied Mathematics, 2014Co-Authors: Shujun Shen, Ian Turner, J ChenAbstract:In this paper, we consider a space fractional advection–dispersion equation. The equation is obtained from the standard advection–diffusion equation by replacing the first- and second-order space derivatives by the Riesz fractional derivatives of order β1 ∈ (0, 1) and β2 ∈ (1, 2], respectively. The fractional advection and dispersion terms are approximated by using two fractional centred difference schemes. A new weighted Riesz fractional finite-difference Approximation scheme is proposed. When the weighting factor θ equals 12, a second-order accuracy scheme is obtained. The stability, consistency and convergence of the Numerical Approximation scheme are discussed. A Numerical example is given to show that the Numerical results are in good agreement with our theoretical analysis.
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Numerical Approximation for a variable-order nonlinear reaction–subdiffusion equation
Science & Engineering Faculty, 2013Co-Authors: Chang-ming Chen, Ian Turner, Y. ChenAbstract:Fractional reaction–subdiffusion equations are widely used in recent years to simulate physical phenomena. In this paper, we consider a variable-order nonlinear reaction–subdiffusion equation. A Numerical Approximation method is proposed to solve the equation. Its convergence and stability are analyzed by Fourier analysis. By means of the technique for improving temporal accuracy, we also propose an improved Numerical Approximation. Finally, the effectiveness of the theoretical results is demonstrated by Numerical examples.
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Numerical Approximation for a variable-order nonlinear reaction---subdiffusion equation
Numerical Algorithms, 2012Co-Authors: Chang-ming Chen, Ian Turner, Y. ChenAbstract:Fractional reaction---subdiffusion equations are widely used in recent years to simulate physical phenomena. In this paper, we consider a variable-order nonlinear reaction---subdiffusion equation. A Numerical Approximation method is proposed to solve the equation. Its convergence and stability are analyzed by Fourier analysis. By means of the technique for improving temporal accuracy, we also propose an improved Numerical Approximation. Finally, the effectiveness of the theoretical results is demonstrated by Numerical examples.
Joseph E Pasciak - One of the best experts on this subject based on the ideXlab platform.
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Numerical Approximation of the integral fractional laplacian
Numerische Mathematik, 2019Co-Authors: Andrea Bonito, Joseph E PasciakAbstract:We propose a new nonconforming finite element algorithm to approximate the solution to the elliptic problem involving the fractional Laplacian. We first derive an integral representation of the bilinear form corresponding to the variational problem. The Numerical Approximation of the action of the corresponding stiffness matrix consists of three steps: (1) apply a sinc quadrature scheme to approximate the integral representation by a finite sum where each term involves the solution of an elliptic partial differential equation defined on the entire space, (2) truncate each elliptic problem to a bounded domain, (3) use the finite element method for the space Approximation on each truncated domain. The consistency error analysis for the three steps is discussed together with the Numerical implementation of the entire algorithm. The results of computations are given illustrating the error behavior in terms of the mesh size of the physical domain, the domain truncation parameter and the quadrature spacing parameter.
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Numerical Approximation of fractional powers of regularly accretive operators
Ima Journal of Numerical Analysis, 2016Co-Authors: Andrea Bonito, Joseph E PasciakAbstract:We study the Numerical Approximation of fractional powers of accretive operators in this paper. Namely, if A is the accretive operator asso- ciated with an accretive sesquilinear form A(·,·) defined on a Hilbert space V contained in L 2 (), we approximate A −� for � 2 (0,1). The fractional powers are defined in terms of the so-called Balakrishnan integral formula. Given a finite element Approximation space VhV, A −� is approximated by A −� hh where Ah is the operator associated with the form A(·,·) restricted to Vh andh is the L 2 ()-projection onto Vh. We first provide error esti- mates for (AA � �h)f in Sobolev norms with index in (0,1) for appropriate f. These results depend on elliptic regularity properties of variational solu- tions involving the form A(·,·) and are valid for the case of less than full elliptic regularity. We also construct and analyze an exponentially convergent SINC quadrature Approximation to the Balakrishnan integral defining A � �hf. Fi- nally, the results of Numerical computations illustrating the proposed method are given.
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Numerical Approximation of fractional powers of regularly accretive operators
arXiv: Numerical Analysis, 2015Co-Authors: Andrea Bonito, Joseph E PasciakAbstract:We study the Numerical Approximation of fractional powers of accretive operators in this paper. Namely, if $A$ is the accretive operator associated with an accretive sesquilinear form $A(\cdot,\cdot)$ defined on a Hilbert space $\mathbb V$ contained in $L^2(\Omega)$, we approximate $A^{-\beta}$ for $\beta\in (0,1)$. The fractional powers are defined in terms of the so-called Balakrishnan integral formula. Given a finite element Approximation space $\mathbb V_h\subset \mathbb V$, $A^{-\beta}$ is approximated by $A_h^{-\beta}\pi_h$ where $A_h$ is the operator associated with the form $A(\cdot,\cdot)$ restricted to $\mathbb V_h$ and $\pi_h$ is the $L^2(\Omega)$-projection onto $\mathbb V_h$. We first provide error estimates for $(A^\beta-A_h^{\beta}\pi_h)f$ in Sobolev norms with index in [0,1] for appropriate $f$. These results depend on elliptic regularity properties of variational solutions involving the form $A(\cdot,\cdot)$ and are valid for the case of less than full elliptic regularity. We also construct and analyze an exponentially convergent sinc quadrature Approximation to the Balakrishnan integral defining $A_h^{\beta}\pi_h f$. Finally, the results of Numerical computations illustrating the proposed method are given.
