Difference Equations by Differential Equation Methods

This book collects research papers from leading world experts in the field, highlighting ongoing trends, progress, and open problems in this critically important area of mathematics.

The book is suitable for readers with a background in basic finite element and finite difference methods for partial differential equations who wants gentle introductions to advanced topics like parallel computing, multigrid methods, and special methods for systems of PDEs. The goal of all chapters is to *compute* solutions to problems, hence algorithmic and software issues play a central role.

In the past few years, the differential quadrature method has been applied extensively in engineering. This book, aimed primarily at practising engineers, scientists and graduate students, gives a systematic description of the mathematical fundamentals of differential quadrature and its detailed implementation in solving Helmholtz problems and problems of flow, structure and vibration.

Delay partial difference equations occur frequently in the approximation of solutions of delay partial differential equations by finite difference methods, random walk problems, the study of molecular orbits and mathematical physics problems.

Delay partial difference equations occur frequently in the approximation of solutions of delay partial differential equations by finite difference methods, random walk problems, the study of molecular orbits and mathematical physics problems. Many results have been done for the qualitative theory of delay partial difference equation in the past ten years. But there has not been a book in the literature presenting the systematical theory on delay partial difference equations so far. This book provides a broad scenario of the qualitative theory of delay partial difference equations.

Construct and solve real-life examples using first-order ordinary differential equations