In this article, Crank-Nicolson method is used to study the variable order fractional cable equation. The variable order fractional derivatives are described in the Riemann- Liouville and the Griinwald-Letnikov sense....In this article, Crank-Nicolson method is used to study the variable order fractional cable equation. The variable order fractional derivatives are described in the Riemann- Liouville and the Griinwald-Letnikov sense. The stability analysis of the proposed technique is discussed. Numerical results are provided and compared with exact solutions to show the accuracy of the proposed technique.展开更多
In this paper,a special case of nonlinear time fractional cable equation is studied.For the equation defined on a bounded domain,the existence,uniqueness,and regularity of the solution are firstly studied.Furthermore,...In this paper,a special case of nonlinear time fractional cable equation is studied.For the equation defined on a bounded domain,the existence,uniqueness,and regularity of the solution are firstly studied.Furthermore,it is numerically studied via the weighted and shifted Grünwald difference(WSGD)methods/the local discontinuous Galerkin(LDG)finite element methods.The derived numerical scheme has been proved to be stable and convergent with order O(t2+hk+1),wheret,h,k are the time stepsize,the spatial stepsize,and the degree of piecewise polynomials,respectively.Finally,a numerical experiment is presented to verify the theoretical analysis.展开更多
文摘In this article, Crank-Nicolson method is used to study the variable order fractional cable equation. The variable order fractional derivatives are described in the Riemann- Liouville and the Griinwald-Letnikov sense. The stability analysis of the proposed technique is discussed. Numerical results are provided and compared with exact solutions to show the accuracy of the proposed technique.
基金supported by the National Natural Science Foundation of China under Grant No.11671251.
文摘In this paper,a special case of nonlinear time fractional cable equation is studied.For the equation defined on a bounded domain,the existence,uniqueness,and regularity of the solution are firstly studied.Furthermore,it is numerically studied via the weighted and shifted Grünwald difference(WSGD)methods/the local discontinuous Galerkin(LDG)finite element methods.The derived numerical scheme has been proved to be stable and convergent with order O(t2+hk+1),wheret,h,k are the time stepsize,the spatial stepsize,and the degree of piecewise polynomials,respectively.Finally,a numerical experiment is presented to verify the theoretical analysis.
