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...

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 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...

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...

Usually, harmonic load flow studies are based on deterministic solutions. Very often, the measured distortion levels are less severe than those predicted by the models but often show the presence of noncharacteristic harmonics that do not exit in simulation results. This is due to the fact that...

In this paper a scheme for approximating solutions of convection–diffusion–reaction equations by Markov jump processes is studied. The general principle of the method of lines reduces evolution partial differential equations to semi-discrete approximations consisting of systems of ordinary...

The paper is concerned with a posteriori error estimates needed for the adaptive construction of a space grid in solving an initial-boundary value one-dimensional problem for a nonlinear parabolic partial differential equation by the method of lines. A posteriori error indicators are introduced...

Piezoelectric ultrasonic motors are superior to electromagnetic micro motors, because their efficiency remains theoretically constant during miniaturization. However, the still relatively recent technology has a considerable unexploited optimisation potential. Numerical structural analysis by...