Advertisement

Differential and Difference Equations

A Comparison of Methods of Solution

  • Leonard C. Maximon
Book

Table of contents

  1. Front Matter
    Pages i-xv
  2. Leonard C. Maximon
    Pages 1-3
  3. Leonard C. Maximon
    Pages 35-37
  4. Leonard C. Maximon
    Pages 39-62
  5. Back Matter
    Pages 125-162

About this book

Introduction

This book, intended for researchers and graduate students in physics, applied mathematics and engineering, presents a detailed comparison of the important methods of solution for linear differential and difference equations - variation of constants, reduction of order, Laplace transforms and generating functions - bringing out the similarities as well as the significant differences in the respective analyses. Equations of arbitrary order are studied, followed by a detailed analysis for equations of first and second order. Equations with polynomial coefficients are considered and explicit solutions for equations with linear coefficients are given, showing significant differences in the functional form of solutions of differential equations from those of difference equations. An alternative method of solution involving transformation of both the dependent and independent variables is given for both differential and difference equations. A comprehensive, detailed treatment of Green’s functions and the associated initial and boundary conditions is presented for differential and difference equations of both arbitrary and second order. A dictionary of difference equations with polynomial coefficients provides a unique compilation of second order difference equations obeyed by the special functions of mathematical physics. Appendices augmenting the text include, in particular, a proof of Cramer’s rule, a detailed consideration of the role of the superposition principal in the Green’s function, and a derivation of the inverse of Laplace transforms and generating functions of particular use in the solution of second order linear differential and difference equations with linear coefficients.

Keywords

Solution of linear differential equations Solution of linear difference equations Wronskian determinant Green’s function and the superposition principle Proof of Cramer's rule Method of variation of constants Casoratian determinant Difference equations Ordinary differential equations Classical hypergeometric functions Confluent hypergeometric functions Special functions of mathematical physics

Authors and affiliations

  • Leonard C. Maximon
    • 1
  1. 1.The George Washington UniversityPhysics DepartmentWashingtonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-29736-1
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-29735-4
  • Online ISBN 978-3-319-29736-1
  • Buy this book on publisher's site
Industry Sectors
Energy, Utilities & Environment