This paper present a novel numerical algorithm for the linear one-dimensional heat and wave equation. In this method, a nite dierenceapproach had been used to discrete the time derivative while cubic spline isapplied as an interpolation function in the space dimension. We discuss theaccuracy of the method by expanding the equation based on Taylor series andminimize the error. The proposed metho...

A stochastic representation of the dynamics of the Burger's turbulence model and of the two{dimensional turbulence is developed. The random velocity eld is regarded as a multivariate stochastic Markov process deened by a master equation. It is shown that Burgers' equation and the two{dimensional Navier{Stokes equation are obtained as the macroscopic equations for the averages of the underlying ...

In this paper, the Chebyshev spectral collocation method(CSCM) for one-dimensional linear hyperbolic telegraph equation is presented. Chebyshev spectral collocation method have become very useful in providing highly accurate solutions to partial differential equations. A straightforward implementation of these methods involves the use of spectral differentiation matrices. Firstly, we transform ...

It is shown that the inverse scattering problem for the three-dimensional SchrSdinger equation with a potential having no spherical symmetry can be solved using a Fredholm integral equation. The integral operator studied here is shown to be compact and self-adjoint with its spectrum in [-1, 1]. The relationship between solutions of this Fredholm equation and of a related RiemannHilbert problem ...

We present the Girsanov theorem for a non linear Itô equation in an infinite dimensional Hilbert space with a non linearity of polynomial growth and an infinite dimensional additive noise. We assume a condition weaker than Novikov one, as done by Mikulevicius and Rozovskii in the study of more general stochastic PDE’s. The equivalence of the laws of the linear equation and of the non linear equ...

As in the finite-dimensional case, the appropriate state feedback for the infinitedimensional H disturbance-attenuation problem may be calculated by solving a Riccati equation. This operator Riccati equation can rarely be solved exactly. We approximate the original infinitedimensional system by a sequence of finite-dimensional systems and consider the corresponding finite-dimensional disturbanc...

Abstract. In this article, we propose a model describing the transport of trapped particles in a surface potential. The potential confines particles close to the surface increasing the number of surface collisions. First, we consider the case of non charged particles. From a kinetic description, we rigorously derive a two dimensional Boltzmann equation. In the case of charged particles we intro...

The object of the present paper is to study temperature distribution and thermal stresses of a functionally graded thick hollow cylinder with temperature dependent material properties. All the material properties except Poisson’s ratio are assumed to be dependent on temperature. The nonlinear heat conduction with temperature dependent thermal conductivity and specific heat capacity is reduced t...

The object of the present paper is to study heat conduction and thermal stresses in a hollow cylinder with nonhomogeneous material properties. The cylinder is subjected to sectional heating at the curved surface. All the material properties except for Poisson’s ratio and density are assumed to be given by a simple power law in the axial direction. A solution of the two-dimensional heat conducti...

In this paper, the oscillating two-dimensional laminar flow about a cylinder and the oscillation of a cylinder in still water are studied. A finite volume method is applied to solve the Navier Stokes equations using SIMPLEC algorithm on a body fitted co-located O-type grid. In this study, the non-dimensional flow numbers, Keulegan-Carpenter and Stokes’ numbers are chosen over a range where diff...