In this paper, the dierential transform method (DTM) is applied to the Fisherequation. This method can be used to obtain the exact solutions of Fisherequation. Finally, we give some examples to illustrate the suciency of themethod for solving such nonlinear partial dierential equations. These resultsshow that this technique is easy to apply.

Several stabilized finite element methods for the Stokes eigenvalue problem based on the lowest equal-order finite element pair are numerically investigated. They are penalty, regular, multiscale enrichment, and local Gauss integration method. Comparisons between them are carried out, which show that the local Gauss integration method has good stability, efficiency, and accuracy properties, and...

In this paper we introduced the Navier-Stokes equations with a boundary (D+N) condition. We have shown the existence and uniqueness of the solution of the weak formulation obtained. We used the discretization by mixed finite element method. In order to evaluate the performance of the method, the numerical results are compared with some previously published works or with others coming from comme...

In this paper, we introduce a mixed finite element method on a staggered mesh for the numerical solution of the steady state Navier-Stokes equations in which the two components of the velocity and the pressure are defined on three different meshes. This method is a conforming quadrilateral Q1 × Q1 − P0 element approximation for the Navier-Stokes equations. First-order error estimates are obtain...

Coherent anti-Stokes Raman scattering (CARS) processes are "coherent," but the phase of the anti-Stokes radiation is lost by most incoherent spectroscopic CARS measurements. We propose a Raman microscopy imaging method called nonlinear interferometric vibrational imaging, which measures Raman spectra by obtaining the temporal anti-Stokes signal through nonlinear interferometry. With a more comp...

A domain decomposition unsteady Stokes solver has been implemented in a hybrid spectral/hp element solver. To extend the algorithm to solve the Navier-Stokes equations the non-linear terms are explicitly advanced in time and treated as a forcing function to the Stokes solver. This scheme is compared with the computa-tionally eecient high order splitting method and it is found that for polynomia...

Stokes phenomenon refers to the fact that an asymptotic expansion of complex functions can differ in different regions of the complex plane, and that beyond the so-called Stokes lines the expansion has an unphysical divergence. An important special case is when the Stokes lines emanate from phase space caustics of a complex trajectory manifold. In this case, symmetry determines that to second o...

Abstract. This paper discusses the symbol of the Hessian of a shape optimization problem in a viscid, incompressible flow. The symbol of the Hessian for the Stokes shape optimization problem is analytically approximated by tracking a Fourier mode through the operators involved. We propose a discrete method for finding the symbol and confirm the correctness by comparison with the analytical data...

The finite element solution of a generalized Stokes system in terms of the flow variables stream function and vorticity is studied. This system results from a time discretization of the time-dependent Stokes system in stream function-vorticity formulation, or yet by the application of the characteristics method to solve the Navier-Stokes equations in the same representation. Numerical results p...

Tchebychev iteration may be used for acceleration convergence of an iterative algorithm to solve a general linear system equation. Associating it with the Uzawa method, we suggest a new iterative solution method for the Stokes problems. The new algorithm retains the simplicity and robustness of the Uzawa method. So it requires almost no additional cost of computation, in terms of storage or CPU...