In this work,we develop a finite difference/finite element method for the two-dimensional distributed-order time-space fractional reaction-diffusion equation(2D-DOTSFRDE)with low regularity solution at the initial tim...In this work,we develop a finite difference/finite element method for the two-dimensional distributed-order time-space fractional reaction-diffusion equation(2D-DOTSFRDE)with low regularity solution at the initial time.A fast evaluation of the distributedorder time fractional derivative based on graded time mesh is obtained by substituting the weak singular kernel for the sum-of-exponentials.The stability and convergence of the developed semi-discrete scheme to 2D-DOTSFRDE are discussed.For the spatial approximation,the finite element method is employed.The convergence of the corresponding fully discrete scheme is investigated.Finally,some numerical tests are given to verify the obtained theoretical results and to demonstrate the effectiveness of the method.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11671343,11601460)the Natural Science Foundation of Hunan Province of China(No.2018JJ3491)the Project of Scientific Research Fund of Hunan Provincial Science and Technology Department,China(No.2018WK4006).
文摘In this work,we develop a finite difference/finite element method for the two-dimensional distributed-order time-space fractional reaction-diffusion equation(2D-DOTSFRDE)with low regularity solution at the initial time.A fast evaluation of the distributedorder time fractional derivative based on graded time mesh is obtained by substituting the weak singular kernel for the sum-of-exponentials.The stability and convergence of the developed semi-discrete scheme to 2D-DOTSFRDE are discussed.For the spatial approximation,the finite element method is employed.The convergence of the corresponding fully discrete scheme is investigated.Finally,some numerical tests are given to verify the obtained theoretical results and to demonstrate the effectiveness of the method.
