The fast progress has been observed in the development of numerical and analytical techniques for solving convection-diffusion and fluid mechanics problems. Here, a numerical approach, based in Galerkin Finite Element Method with Finite Difference Method is presented for the solution of a class of non-linear transient convection-diffusion problems. Using the analytical solutions and the L2 and ...

In the present work, a framework is developed for implementation of finite difference schemes on Graphic Processing Units (GPU). The framework is developed using the CUDA language and C++ template meta-programming techniques. The framework is also applicable for other numerical methods which can be represented similar to finite difference schemes such as finite volume methods on structured grid...

The enhancement of the perpendicular temperature inside the resonant region, observed in numerical studies of the two-dimensional Fokker-Planck equation, combined with unidirectional RF quasilinear diffusion, is modeled on the basis of the collisional relaxation equations. Strong RF diffusion is assumed and relativistic effects are taken into account. The resulting enhanced perpendicular temper...

In this article we analyze a fully discrete numerical approximation to a time dependent fractional order diffusion equation which contains a non-local, quadratic non-linearity. The analysis is performed for a general fractional order diffusion operator. The non-linear term studied is a product of the unknown function and a convolution operator of order 0. Convergence of the approximation and a ...

Abstract — A survey is given of current research into the numerical solution of timeindependent systems of second-order differential equations whose diffusion coefficients are small parameters. Such problems are in general singularly perturbed. The equations in these systems may be coupled through their reaction and/or convection terms. Only numerical methods whose accuracy is guaranteed for al...

I wish to develop the phenomenological diffusion model of interaction of gravitational waves on water surface in presence of wind and viscosity. Motivation for development of such a model is the fact that numerical solvers based on Hasselmann kinetic equation for waves are time-consuming and hardly can be used for practical purposes. Numerical solver based on the diffusion model is expected to ...

In this work we show some results about the reduced basis approximation of advection dominated parametrized problems, i.e. advection-diffusion problems with high Péclet number. These problems are of great importance in several engineering applications and it is well known that their numerical approximation can be affected by instability phenomena. In this work we compare two possible stabilizat...

Abstract In this paper, we study the numerical solutions of Fisher’s equation and to a nonlinear diffusion equation of the Fisher type by differential quadrature method. Fisher's equation combines diffusion with logistic nonlinearity. The equation occurs in logistic population growth models, neurophysiology and nuclear reactions. Therefore, numerical study of these types of equations is very im...

A theoretical analysis tool, iterated optimal stopping, has been used as the basis of a numerical algorithm for American options under regime switching [19]. Similar methods have also been proposed for American options under jump diffusion [3] and Asian options under jump diffusion [4]. We show that a re-arrangement of the numerical algorithm in the form of local policy iteration [21, 17] has p...

A class of second order approximations, called the weighted and shifted Grünwald difference operators, are proposed for Riemann-Liouville fractional derivatives, with their effective applications to numerically solving space fractional diffusion equations in one and two dimensions. The stability and convergence of our difference schemes for space fractional diffusion equations with constant coe...