Nasir Ali

Discrete Symmetries for the Higher Dimensional Heat Equation Nasir Ali

Difference equations are very useful in daily life. There are lot of applications of difference equations in business, statistics, economics, computer programming and numerical solutions of differential equations. In mathematics, there are two reasons for using the difference equations. Firstly, difference equations play an important role in the designing of mathematical models which are used in mechanics and mathematical physics. Such kind of models relay on symmetries. The existence of exact analytical solution of the difference equation and their conservation laws are related to their continuous symmetries. Secondly, in the theory of differential equation (D. E), system of D. E. can be replaced by using difference equations and meshes. In this book, a complete symmetry analysis for the multidimensional discrete heat equation is presented. For this, generalized prolongations are reported for the considered equation. Furthermore, Lie point generators are computed for n=2, 3 and then generalized for the arbitrary value of n. A relationship between the number of the symmetries and the value of n is given at last.