Complex Ginzburg–Landau Equation with Generalized Finite Differences

A Parseval equation and a generalized finite Hankel transformation

In this paper, we study the finite Hankel transformation on spaces of generalized functions by developing a new procedure. We consider two Hankel type integral transformations hμ and h∗μ connected by the Parseval equation

Holistic finite differences ensure fidelity to Burger’s equation

I analyse a generalised Burger’s equation to develop an accurate finite difference approximation to its dynamics. The analysis is based upon centre manifold theory so we are assured that the finite difference model accurately models the dynamics and may be constructed systematically. The trick to the application of centre manifold theory is to divide the physical domain into small elements by i...

Discretization of Electromagnetic Problems: The “Generalized Finite Differences” Approach

Bifurcation and of the Generalized Complex Ginzburg–landau Equation

We study in this paper the bifurcation and stability of the solutions of the complex Ginzburg–Landau equation(CGLE). We investigate two different modes of CGLE. We study the first mode of CGLE which has only cubic unstable nonlinear term and later we also study the second mode of CGLE which has both cubic and quintic nonlinear terms. The solutions considered in cubic CGLE bifurcate from the tri...

Finite-Time Blowup for a Complex Ginzburg-Landau Equation

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