Boundary value problems for third-order nonlinear ordinary differential equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here

Boundary value problems for third-order nonlinear ordinary differential equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here

Analysis of modified Reynolds equation using the wavelet-multigrid scheme

The combined study of effects of surface roughness and poroelasticity on the squeeze film behavior of bearings in general and that of synovial joints in particular are presented. The modified form of Reynolds equation, which incorporates the randomized roughness structure as well as elastic nature of articular cartilage, is derived. Christensen stochastic theory describing roughness structure of cartilage surfaces is used by assuming the roughness asperity heights to be small compared to the film thickness. A recently developed wavelet-multigrid method is used for the solution of Reynolds equation. The method has the greatest advantage of minimizing the errors using wavelet transforms in obtaining accurate solution, as grid size tends to zero. Based on the results obtained, the influence of roughness and elasticity on bearing characteristics are discussed in some detail. (c) 2006 Wiley Periodicals, Inc