Thesis Topic:
Analytical and Numerical solution of viscous burger's equation
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Hi, i am Ronobir Chandra Sarker from Jahangirnagar University, Dhaka, Bangladesh. I studyed in Department of Mathematics of this university. I completed my research about Burger Equation
The one-dimensional Burger's equation has received an enormous amount of at-
tention since the studies by J.M. Burger's in the 1940's, principally as a model
problem of the interaction between nonlinear and dissipative phenomena. Even
though it is a simplest case study' which in many setting is not realistic, it has
been important in wide range of mathematical problems, from hydrodynamics to
geometry. It is now realized that Burger's equation was used by a number of scien-
tists before its re-introduction by Burgers, for example see H. Beteman([5],1915)
and A.R. Forsyth([6],1906,pp.97-102).
It is now known that it was rst introduced by Bateman[7] in 1915 who found
its steady solutions, descriptive of certain viscous ows. It was later proposed
by Burgers as one of a class of equations describing mathematical models of tur-
bulence and due to the extensive work of Burger it is now known as Burger's
equation. In the content of gas dynamics, it was discussed by Hopf and Cole.
They also illustrated independently that the Burger's equation can be solved ex-
actly for an arbitrary initial condition. Benton and Platzman have surveyed the
analytical solutions of the one dimensional Burgers equation. It can be considered
as a simpli ed form of the Navier-Stokes equation due to the form of non-linear
convection term and the occurrence of the viscosity term.
In order to understand the non-linear phenomenon of the Navier-Stokes equa-
tion, one needs to study Burger's equation analytically and numerically as well.
Many works has been appeared in the last several years e.g. [9],[10],[11] etc.
In this thesis work, we present the analytical solution of one-dimensional Burger's
equation as an initial value problem in in nite spatial domain and some numerical
methods for solution of Burger's equation as an initial boundary value problem.
We design the thesis work as follows