6 papers
Optimal preconditioning techniques for finite volume approximation of three-dimensional conservative space-fractional diffusion equations
Wei Qu, Siu-Long Lei, Sean Y. Hon +1
A Crank-Nicolson finite volume approximation for three-dimensional conservative space-fractional diffusion equation results in large and dense three-level Toeplitz discrete linear…
An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients
Yuan-Yuan Huang, Wei Qu, Sean Y. Hon +1
In this paper, we propose an efficient method for solving multi-dimensional Riesz space fractional diffusion equations with variable coefficients. The Crank-Nicolson (CN) method is…
Upwind-and-shifted numerical scheme for fractional convection equation
Lot-Kei Chou, Wan-Na Deng, Yuan-Yuan Huang +1
Fundamental solution of a space fractional convection equation of order is the probability density function of Lévy flights with long-tailed -stable jump length distribution…
Optimal preconditioners for nonsymmetric multilevel Toeplitz systems with application to solving non-local evolutionary partial differential equations
Yuan-Yuan Huang, Sean Y. Hon, Lot-Kei Chou +1
Preconditioning for multilevel Toeplitz systems has long been a focal point of research in numerical linear algebra. In this work, we develop a novel preconditioning method for a c…
An efficient preconditioner for evolutionary partial differential equations with -method in time discretization
Yuan-Yuan Huang, Po Yin Fung, Sean Y. Hon +1
In this study, the -method is used for discretizing a class of evolutionary partial differential equations. Then, we transform the resultant all-at-once linear system and introd…
A novel fourth-order scheme for two-dimensional Riesz space fractional nonlinear reaction-diffusion equations and its optimal preconditioned solver
Wei Qu, Yuan-Yuan Huang, Sean Hon +1
A novel fourth-order finite difference formula coupling the Crank-Nicolson explicit linearized method is proposed to solve Riesz space fractional nonlinear reaction-diffusion equat…