scholarly journals Preconditioned iterative methods for space-time fractional advection-diffusion equations

2016 ◽  
Vol 319 ◽  
pp. 266-279 ◽  
Author(s):  
Zhi Zhao ◽  
Xiao-Qing Jin ◽  
Matthew M. Lin
Keyword(s):  
Iterative Methods ◽  
Space Time ◽  
Diffusion Equations ◽  
Advection Diffusion ◽  
Preconditioned Iterative ◽  
Preconditioned Iterative Methods

Preconditioned Iterative Methods for Two-Dimensional Space-Fractional Diffusion Equations

2015 ◽  
Vol 18 (2) ◽  
pp. 469-488 ◽  
Author(s):  
Xiao-Qing Jin ◽  
Fu-Rong Lin ◽  
Zhi Zhao
Keyword(s):  
Linear Systems ◽  
Iterative Methods ◽  
Dimensional Space ◽  
Fractional Diffusion ◽  
Second Order ◽  
Diffusion Equations ◽  
Two Dimensional ◽  
Fractional Diffusion Equations ◽  
Preconditioned Iterative ◽  
Preconditioned Iterative Methods

AbstractIn this paper, preconditioned iterative methods for solving two-dimensional space-fractional diffusion equations are considered. The fractional diffusion equation is discretized by a second-order finite difference scheme, namely, the Crank-Nicolson weighted and shifted Grünwald difference (CN-WSGD) scheme proposed in [W. Tian, H. Zhou and W. Deng, A class of second order difference approximation for solving space fractional diffusion equations, Math. Comp., 84 (2015) 1703-1727]. For the discretized linear systems, we first propose preconditioned iterative methods to solve them. Then we apply the D’Yakonov ADI scheme to split the linear systems and solve the obtained splitting systems by iterative methods. Two preconditioned iterative methods, the preconditioned generalized minimal residual (preconditioned GMRES) method and the preconditioned conjugate gradient normal residual (preconditioned CGNR) method, are proposed to solve relevant linear systems. By fully exploiting the structure of the coefficient matrix, we design two special kinds of preconditioners, which are easily constructed and are able to accelerate convergence of iterative solvers. Numerical results show the efficiency of our preconditioners.

Analytical solutions of the space–time fractional Telegraph and advection–diffusion equations

2018 ◽  
Vol 491 ◽  
pp. 810-819 ◽  
Author(s):  
Ashraf M. Tawfik ◽  
Horst Fichtner ◽  
Reinhard Schlickeiser ◽  
A. Elhanbaly
Keyword(s):  
Analytical Solutions ◽  
Space Time ◽  
Diffusion Equations ◽  
Advection Diffusion

Verification of Iterative Methods for the Linear Complementarity Problem

2016 ◽  
pp. 545-580 ◽  
Author(s):  
H. Saberi Najafi ◽  
S. A. Edalatpanah
Keyword(s):  
Fixed Point ◽  
Iterative Methods ◽  
Linear Complementarity Problem ◽  
Numerical Experiments ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Convergence Results ◽  
Fixed Point Principle ◽  
Preconditioned Iterative ◽  
Preconditioned Iterative Methods

In the present chapter, we give an overview of iterative methods for linear complementarity problems (abbreviated as LCPs). We also introduce these iterative methods for the problems based on fixed-point principle. Next, we present some new properties of preconditioned iterative methods for solving the LCPs. Convergence results of the sequence generated by these methods and also the comparison analysis between classic Gauss-Seidel method and preconditioned Gauss-Seidel (PGS) method for LCPs are established under certain conditions. Finally, the efficiency of these methods is demonstrated by numerical experiments. These results show that the mentioned models are effective in actual implementation and competitive with each other.

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