We propose a multiscale finite element method for solving second order elliptic equations with rapidly oscillating coefficients. The main purpose is to design a numerical method which is capable of correctly capturing the large scale components of the solution on a coarse grid without accurately resolving all the small scale features in the solution. This is accomplished by incorporating the lo...

An exact solution of unsteady free convective and mass transfer flow through porous medium bounded by a vertical porous plate with an oscillating free stream velocity is obtained. The entire system rotates about an axis normal to the plate. Existence of multiple Ekman boundary layer modified by the presence of free convection and mass transfer is observed near the neighbourhood of plate wall.

We study a hard regime of stimulation of two-frequency oscillations in the main resonance equation with a fast oscillating external force: εiψ ′ + |ψ| 2 ψ = exp (it 2 /(2ε)), 0 < ε ≪ 1. This phenomenon is caused by resonance between an eigenmode and the external force. The asymptotic solution before, inside and after the resonance layer is studied in detail and matched.

In this paper, we study a nonlinear heat equation with a periodic timeoscillating term in factor of the nonlinearity. In particular, we give examples showing how the behavior of the solution can drastically change according to both the frequency of the oscillating factor and the size of the initial value.

In this paper, we propose the Chebyshev wavelet approximation for the numerical solution of a class of integrodifferential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields. We show that the Chebyshev approximation transform an integral equation to an explicit system of linear algebraic equations. Illustrative examples are included to...

We consider the elasticity problem in a heterogeneous domain with an ε-periodic micro-structure, ε 1, including multiple micro-contacts between the structural components. These components can be a simply connected matrix domain with open cracks or inclusions completely surrounded by cracks, which do not touch the outer boundary. The contacts are described by the Signorini and Tresca-friction co...

A natural approach for solving large, high-frequency scattering problems is to augment a numerical (simulated) solution with the notion that light travels as rays. This combines the robustness of numerical methods, where every detail of the problem is modeled in the computer, with the quick timeto-solution characteristic of ray models. The resulting algorithms have potential to reduce overall c...

This paper proposes a solution to the problem of velocity and position estimation for a class of oscillating systems whose position, velocity and acceleration are zero mean signals. The proposed scheme considers that the dynamic model of the system is unknown and only noisy acceleration measurements are available.