Qamar Din

Invariant Solutions: Invariant Solutions of Difference Equations Qamar Din

Mathematics models real life phenomena to understand the underlying laws of nature governing them, more precisely. Ever changing physical phenomena are represented by differential equations. But this imposes condition that the changes itself are continuous and are taking place in a continuous domain. Whereas real situation, most of the times, are discrete in nature. These phenomena are present in almost everywhere but most commonly in Biology, Physics (classical and quantum), Geometry, Mathematical design and Finance etc. Difference equations provide a better choice to represent discrete Phenomena. This makes difference equations an important mathematical object to understand. But theory of difference equation is not as developed as differential equations. Symmetry analysis provides an algorithmic method to integrate differential equation. Many authors have applied this method to integrate difference equations. This book quickly introduces difference equation and their symmetry analysis. Hopefully, this book will help graduate students to begin their research in this field.