Difference Equations by Differential Equation Methods
Most well-known solution techniques for differential equations exploit symmetry in some form. Systematic methods have been developed for finding and using symmetries, first integrals and conservation laws of a given differential equation. Here the author explains how to extend these powerful methods to difference equations, greatly increasing the range of solvable problems. Beginning with an introduction to elementary solution methods, the book gives readers a clear explanation of exact techniques for ordinary and partial difference equations. The informal presentation is suitable for anyone who is familiar with standard differential equation methods. No prior knowledge of difference equations or symmetry is assumed. The author uses worked examples to help readers grasp new concepts easily. There are 120 exercises of varying difficulty and suggestions for further reading. The book goes to the cutting edge of research; its many new ideas and methods make it a valuable reference for researchers in the field.
In computational mechanics, the first and quite often the most difficult part of a problem is the correct formulation of the problem. This is usually done in terms of differential equations. Once...
The study of oscillatory phenomena is an important part of the theory of differential equations. Oscillations naturally occur in virtually every area of applied science including, e.g., mechanics,...
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of...