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	High-Order Accurate Runge-Kutta (Local) Discontinuous Galerkin Methods for One- and Two-Dimensional Fractional Diffusion Equations
	Ji, Xia ; Tang, Huazhong
	2012
关键词	Discontinuous Galerkin method Runge-Kutta time discretization fractional derivative Caputo derivative diffusion equation FINITE-ELEMENT-METHOD PARTIAL-DIFFERENTIAL-EQUATIONS ADVECTION-DISPERSION EQUATION FOKKER-PLANCK EQUATION CONSERVATION-LAWS RANDOM-WALKS SYSTEMS SPACE
英文摘要	As the generalization of the integer order partial differential equations (PDE), the fractional order PDEs are drawing more and more attention for their applications in fluid flow, finance and other areas. This paper presents high-order accurate Runge-Kutta local discontinuous Galerkin (DG) methods for one-and two-dimensional fractional diffusion equations containing derivatives of fractional order in space. The Caputo derivative is chosen as the representation of spatial derivative, because it may represent the fractional derivative by an integral operator. Some numerical examples show that the convergence orders of the proposed local P-k-DG methods are O(h(k+1)) both in one and two dimensions, where P-k denotes the space of the real-valued polynomials with degree at most k.; Mathematics, Applied; Mathematics; SCI(E); 0; ARTICLE; 3; 333-358; 5
语种	英语
出处	SCI
出版者	numerical mathematics theory methods and applications
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/393128]
专题	数学科学学院
推荐引用方式 GB/T 7714	Ji, Xia,Tang, Huazhong. High-Order Accurate Runge-Kutta (Local) Discontinuous Galerkin Methods for One- and Two-Dimensional Fractional Diffusion Equations. 2012-01-01.

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