A finite element method for time fractional partial differential equations

A Finite Element Method for Time Fractional Partial Differential Equations

In this paper, we consider the finite element method for time fractional partial differential equations. The existence and uniqueness of the solutions are proved by using the Lax-Milgram Lemma. A time stepping method is introduced based on a quadrature formula approach. The fully discrete scheme is considered by using a finite element method and optimal convergence error estimates are obtained....

Finite difference method for solving partial integro-differential equations

In this paper, we have introduced a new method for solving a class of the partial integro-differential equation with the singular kernel by using the finite difference method. First, we employing an algorithm for solving the problem based on the Crank-Nicholson scheme with given conditions. Furthermore, we discrete the singular integral for solving of the problem. Also, the numerical results ob...

Finite Element Method for Linear Multiterm Fractional Differential Equations

A New Mixed Element Method for a Class of Time-Fractional Partial Differential Equations

A kind of new mixed element method for time-fractional partial differential equations is studied. The Caputo-fractional derivative of time direction is approximated by two-step difference method and the spatial direction is discretized by a new mixed element method, whose gradient belongs to the simple (L (2)(Ω)(2)) space replacing the complex H(div; Ω) space. Some a priori error estimates in L...

Stability and Convergence of an Effective Finite Element Method for Multiterm Fractional Partial Differential Equations

and Applied Analysis 3 Here B(I × Ω) is a Banach space with respect to the following norm: ‖V‖Bα/2(I×Ω) = (‖V‖ 2 Hα/2(I,L2(Ω)) + ‖V‖ 2 L2(I,H 1 0 (Ω)) ) 1/2 , (15) whereH(I, L2(Ω)) :={V; ‖V(t, L2(Ω) ∈ H α/2 (I)}, endowed with the norm ‖V‖Hα/2(I,L2(Ω)) := 󵄩󵄩󵄩󵄩 ‖V (t, L2(Ω) 󵄩󵄩󵄩󵄩Hα/2(I) . (16) Based on the relation equation between the left Caputo and the Riemann-Liouville derivative in [31], we c...