The Stability of Roll Solutions of the Two-Dimensional Swift–Hohenberg Equation and the Phase-Diffusion Equation

1996 ◽  
Vol 27 (5) ◽  
pp. 1311-1335 ◽  
Author(s):  
Masataka Kuwamura
Keyword(s):  
Diffusion Equation ◽  
Two Dimensional ◽  
Phase Diffusion ◽  
The Stability

scholarly journals ON THE STABILITY CONDITIONS OF 2D TIME FRACTIONAL DIFFUSION EQUATION

2020 ◽  
Vol 25 (1) ◽  
pp. 11-15 ◽  
Author(s):  
Adel Rashed A. Ali Alsabbagh ◽  
Esraa Abbas Al-taai
Keyword(s):  
Diffusion Equation ◽  
Time Derivative ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Stability Conditions ◽  
Two Dimensional ◽  
Time Fractional Diffusion Equation ◽  
The Stability ◽  
Definition Of ◽  
Good Agreement

The Caputo definition of fractional derivative has been employed for the time derivative for the two-dimensional time-fractional diffusion equation. The stability condition obtained by reformulation the classical multilevel technique on the finite difference scheme. A numerical example gives a good agreement with the theoretical result

scholarly journals A new compact alternating direction implicit method for solving two dimensional time fractional diffusion equation with Caputo-Fabrizio derivative

Filomat ◽  
2020 ◽  
Vol 34 (11) ◽  
pp. 3609-3626
Author(s):  
Mehran Taghipour ◽  
Hossein Aminikhah
Keyword(s):  
Diffusion Equation ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Stability And Convergence ◽  
Two Dimensional ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Time Fractional Diffusion Equation ◽  
The Stability ◽  
Theoretical Considerations

In this paper, a new compact alternating direction implicit (ADI) difference scheme is proposed for the solution of two dimensional time fractional diffusion equation. Theoretical considerations are discussed. We show that the proposed method is fourth order accurate in space and two order accurate in time. The stability and convergence of the compact ADI method are presented by the Fourier analysis method. Numerical examples confirm the theoretical results and high accuracy of the proposed scheme.

scholarly journals The two-dimensional hydrodynamical theory of moving aerofoils. IV

1947 ◽  
Vol 188 (1015) ◽  
pp. 439-463
Keyword(s):  
Stability Problem ◽  
Two Dimensional ◽  
Centre Of Gravity ◽  
First Approximation ◽  
Von Karman ◽  
Moving Cylinder ◽  
Period Equation ◽  
The Stability ◽  
Von Kármán ◽  
Hydrodynamical Theory

In the first part of this paper opportunity has been taken to make some adjustments in certain general formulae of previous papers, the necessity for which appeared in discussions with other workers on this subject. The general results thus amended are then applied to a general discussion of the stability problem including the effect of the trailing wake which was deliberately excluded in the previous paper. The general conclusion is that to a first approximation the wake, as usually assumed, has little or no effect on the reality of the roots of the period equation, but that it may introduce instability of the oscillations, if the centre of gravity of the element is not sufficiently far forward. During the discussion contact is made with certain partial results recently obtained by von Karman and Sears, which are shown to be particular cases of the general formulae. An Appendix is also added containing certain results on the motion of a vortex behind a moving cylinder, which were obtained to justify certain of the assumptions underlying the trail theory.

scholarly journals Numerical Analysis WSGD Scheme for One- and Two-Dimensional Distributed Order Fractional Reaction–Diffusion Equation with Collocation Method via Fractional B-Spline

2021 ◽  
Vol 7 (2) ◽  
Author(s):  
Mohammad Ramezani
Keyword(s):  
Diffusion Equation ◽  
Collocation Method ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
B Spline ◽  
Computational Work ◽  
Distributed Order ◽  
Fractional Reaction

AbstractThe main propose of this paper is presenting an efficient numerical scheme to solve WSGD scheme for one- and two-dimensional distributed order fractional reaction–diffusion equation. The proposed method is based on fractional B-spline basics in collocation method which involve Caputo-type fractional derivatives for $$0 < \alpha < 1$$ 0 < α < 1 . The most significant privilege of proposed method is efficient and quite accurate and it requires relatively less computational work. The solution of consideration problem is transmute to the solution of the linear system of algebraic equations which can be solved by a suitable numerical method. The finally, several numerical WSGD Scheme for one- and two-dimensional distributed order fractional reaction–diffusion equation.

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