M.Sc. Project and Dissertation

M.Sc. III Semester Project 

• Similarity Solutions of Partial Differential Equations

Description: The Order of the Partial Differential Equation is reduced by using appropriate Transform- -ations to convert it into Ordinary Differential Equation and thereby solve them. This reduction is called similarity reduction of the PDEs and the used Transformations are called Lie-group of Transformations. The property of the transformations is that the given PDE is invariant under these transformations. The similarity reductions of PDE may be used as a tool for finding changes of variables, which convert the original PDE in to another PDE. In this manner our original PDE reduces to an Ordinary Differential Equation, which can be, solve easily by conventional methods.

Guide during Project: The project was completed under the valuable guidance of Dr. Y.K. Gupta, Professor, Department of Mathematics, Indian Institute of Technology Roorkee, India.

Tel: +91 - 1332 - 285761, E-mail: kumarfma@iitr.ernet.in

M.Sc. IV Semester Project

• • Direct Methods of Calculus of Variations for Solving Partial Differential Equations

Description: To identify the various methods which are possible so that a Partial Differential Equation is solved directly without using any Numerical Method. So these are the techniques of solving a Boundary Value Problem approximately by assuming a trial solution satisfying the given boundary conditions. This trial solution will contain certain parameters, which can be adjusted to minimize the errors so that the trial solution is as close to the exact solution as possible. So these methods give us Approximate Solution of Partial Differential Equation.

Guide during Dissertation: The dissertation was completed under the valuable guidance of Dr. Y.K. Gupta, Professor, Department of Mathematics, Indian Institute of Technology Roorkee, India.

Tel: +91 - 1332 - 285761, E-mail: kumarfma@iitr.ernet.in