Overview

Nonlinear differential equations describe many physical phenomena in fluid dynamics and the investigation of the exact solutions of such nonlinear equations play an impor- tant role in understanding several engineering processes. In general, it is difficult to solve nonlinear problems analytically since there are no general techniques that work for all types of equations. Recently, computers have played a great role in nonlinear science and this has caused a revolution in understanding of nonlinear problems. The studies using numerical simulation picturise the solutions of nonlinear equations very well to gain insights into their behavior and to suggest directions for future analytic research. For some non linear differential equations, it is possible to write down their special solutions explicitly in terms of elementary functions. One way of finding such explicit solutions is to reduce them to equations of lower dimension, preferably ordinary dif- ferential equations, which can often be solved exactly. But there still remains certain systems for which general solutions have not been found both analytically and numer- ically. One such equation is the well known Navier-Stokes equations that govern most of the flow phenomena. These equations are simultaneous system of partial differen- tial equations which are highly nonlinear. Its simpler version known as Boundary layer equations present a great insight to several flow analysis.

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