Convergence analysis of moving finite element methods for space fractional differential equations

Finite difference Methods for fractional differential equations

In this review paper, the finite difference methods (FDMs) for the fractional differential equations are displayed. The considered equations mainly include the fractional kinetic equations of diffusion or dispersion with time, space and time-space derivatives. In some way, these numerical methods have similar form as the case for classical equations, some of which can be seen as the generalizat...

Convergence analysis of spectral Tau method for fractional Riccati differential equations

‎In this paper‎, ‎a spectral Tau method for solving fractional Riccati‎ ‎differential equations is considered‎. ‎This technique describes‎ ‎converting of a given fractional Riccati differential equation to a‎ ‎system of nonlinear algebraic equations by using some simple‎ ‎matrices‎. ‎We use fractional derivatives in the Caputo form‎. ‎Convergence analysis of the proposed method is given an...

Adaptive finite element methods for differential equations

Gegenstand des Buches ist die Dual Weighted Residual method (DWR), ein sehr effizientes numerisches Verfahren zur Behandlung einer großen Klasse von variationell formulierten Differentialgleichungen. Das numerische Verfahren ist adaptiv, d.h. es konstruiert eigenständig eine Folge von Approximationen für eine gegebene Fragestellung. Typische Fragestellungen sind die Bestimmung gewichteter Mitte...

CONVERGENCE ANALYSIS OF FINITE ELEMENT METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS IN NON-DIVERGENCE FORM by

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...