A Galerkin finite element approximation of Wick-stochastic water waves is developed and numerically investigated. The problems under study consist of a class of shallow water equations driven by white noise. Random effects may appear in the water free surface or in the bottom topography among...

In this paper, Lp convergence and almost sure convergence of the Milstein approximation of a partial differential equation of advection–diffusion type driven by a multiplicative continuous martingale is proven. The (semidiscrete) approximation in space is a projection onto a finite dimensional...

In this letter, energy transfer of Jeffery-Hamel nanofluid flow in non-parallel walls is investigated analytically using Galerkin method. The effective thermal conductivity and viscosity of nanofluid are calculated by the Maxwell-Garnetts (MG) and Brinkman models, respectively. The influence of...

This paper advocates a regime-switching model to capture the risk of structural changes in the economy, when determining the optimal bid-ask spread in limit order books. In our model, the market-maker faces an inventory risk due to the diffusive nature of the stocks¡¯ mid-price and a...

A flexible solution method for the initial-boundary value problem of the temperature field in a one-dimensional domain of a solid with significantly nonlinear material parameters and radiation boundary conditions is proposed. A transformation of the temperature values allows the isolation of the...

The coupled nonlinear Schrödinger equation models several interesting physical phenomena presents a model equation for optical fiber with linear birefringence. In this paper we derive a finite element scheme to solve this equation, we test this method for stability and accuracy, many numerical...

This paper presents a velocity/pressure/function-of-transformation formulation to simulate two- and three-dimensional flows by a finite element Galerkin technique associated to stream-tube analysis. The latter method involves an unknown transformation. Applications are given for plane and...

The dependence of total population and population distribution on the spatial distribution of the intrinsic growth factor is studied. The existence of solutions of a nonlinear single species and the corresponding predator-prey model is established. The solutions are then approximated by the...

A general circulation model using a full-Galerkin method is developed for the simulation of atmospheric climate and variability. Two variants of the Galerkin method, the spectral-transform method and the finite-element method, are used in this model for the horizontal and vertical...