TITLE:
Travelling Waves: Interplay of Low to High Reynolds Number and Tan-Cot Function Method to Solve Burger’s Equations
AUTHORS:
Md. Kamrujjaman, Asif Ahmed, Jahrul Alam
KEYWORDS:
Nonlinear PDEs, Tan-Cot Function Method, Travelling Wave Solutions, Burg-er’s Equation, Reynolds Number, Crank-Nicolson Scheme
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.7 No.4,
April
19,
2019
ABSTRACT: We study the nonlinear parabolic
equations for travelling wave solutions of Burger’s equations. The purpose of
the present work is to study various types of Burger’s equations describing
waves and those are based on nonlinear equations. We focus on to describe the
analytic solution in the special pattern of travelling wave solutions using
tan-cot function method. We discuss about inviscid and viscous version of
Burger’s equation for fluid flow and investigate the effects of internal
friction of a fluid via Reynolds number. By changing the velocity amplitude,
the nature of flows with shock wave and disturbance are observed. For numerical
solutions, the Crank-Nicolson scheme is introduced to establish the wave
solutions.