Difference Equations

Difference Equations : Theory, Applications and Advanced Topics, Third Edition

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Difference Equations: Theory, Applications and Advanced Topics, Third Edition provides a broad introduction to the mathematics of difference equations and some of their applications. Many worked examples illustrate how to calculate both exact and approximate solutions to special classes of difference equations. Along with adding several advanced topics, this edition continues to cover general, linear, first-, second-, and n-th order difference equations; nonlinear equations that may be reduced to linear equations; and partial difference equations. New to the Third Edition New chapter on special topics, including discrete Cauchy-Euler equations; gamma, beta, and digamma functions; Lambert W-function; Euler polynomials; functional equations; and exact discretizations of differential equationsNew chapter on the application of difference equations to complex problems arising in the mathematical modeling of phenomena in engineering and the natural and social sciences Additional problems in all chaptersExpanded bibliography to include recently published texts related to the subject of difference equations Suitable for self-study or as the main text for courses on difference equations, this book helps readers understand the fundamental concepts and procedures of difference equations. It uses an informal presentation style, avoiding the minutia of detailed proofs and formal explanations.show more

Product details

  • Paperback
  • Taylor & Francis Ltd
  • CRC Press
  • London, United Kingdom
  • English
  • New edition
  • 3rd New edition
  • 1138894230
  • 9781138894235

Table of contents

THE DIFFERENCE CALCULUS GENESIS OF DIFFERENCE EQUATIONS DEFINITIONS DERIVATION OF DIFFERENCE EQUATIONS EXISTENCE AND UNIQUENESS THEOREM OPERATORS â AND E ELEMENTARY DIFFERENCE OPERATORS FACTORIAL POLYNOMIALS OPERATOR â â 1 AND THE SUM CALCULUS FIRST-ORDER DIFFERENCE EQUATIONS INTRODUCTION GENERAL LINEAR EQUATION CONTINUED FRACTIONS A GENERAL FIRST-ORDER EQUATION: GEOMETRICAL METHODS A GENERAL FIRST-ORDER EQUATION: EXPANSION TECHNIQUES LINEAR DIFFERENCE EQUATIONSINTRODUCTION LINEARLY INDEPENDENT FUNCTIONS FUNDAMENTAL THEOREMS FOR HOMOGENEOUS EQUATIONSINHOMOGENEOUS EQUATIONS SECOND-ORDER EQUATIONS STURM-LIOUVILLE DIFFERENCE EQUATIONS LINEAR DIFFERENCE EQUATIONS INTRODUCTION HOMOGENEOUS EQUATIONS CONSTRUCTION OF A DIFFERENCE EQUATION HAVING SPECIFIED SOLUTIONS RELATIONSHIP BETWEEN LINEAR DIFFERENCE AND DIFFERENTIAL EQUATIONS INHOMOGENEOUS EQUATIONS: METHOD OF UNDETERMINED COEFFICIENTS INHOMOGENEOUS EQUATIONS: OPERATOR METHODS z-TRANSFORM METHOD SYSTEMS OF DIFFERENCE EQUATIONS LINEAR PARTIAL DIFFERENCE EQUATIONS INTRODUCTION SYMBOLIC METHODS LAGRANGE'S AND SEPARATION-OF-VARIABLES METHODS LAPLACE'S METHOD PARTICULAR SOLUTIONS SIMULTANEOUS EQUATIONS WITH CONSTANT COEFFICIENTS NONLINEAR DIFFERENCE EQUATIONS INTRODUCTION HOMOGENEOUS EQUATIONS RICCATI EQUATIONS CLAIRAUT'S EQUATION NONLINEAR TRANSFORMATIONS, MISCELLANEOUS FORMS PARTIAL DIFFERENCE EQUATIONS APPLICATIONS INTRODUCTION MATHEMATICS PERTURBATION TECHNIQUES STABILITY OF FIXED POINTS THE LOGISTIC EQUATION NUMERICAL INTEGRATION OF DIFFERENTIAL EQUATIONS PHYSICAL SYSTEMS ECONOMICS WARFAREBIOLOGICAL SCIENCES SOCIAL SCIENCES MISCELLANEOUS APPLICATIONS ADVANCED TOPICSINTRODUCTION GENERALIZED METHOD OF SEPARATION OF VARIABLESCAUCHY-EULER EQUATION GAMMA AND BETA FUNCTIONS LAMBERT-W FUNCTION THE SYMBOLIC CALCULUS MIXED DIFFERENTIAL AND DIFFERENCE EQUATIONSEULER POLYNOMIALS FUNCTIONAL EQUATIONSFUNCTIONAL EQUATION f(x)2 + g(x)2 = 1 EXACT DISCRETIZATIONS OF DIFFERENTIAL EQUATIONS ADVANCED APPLICATIONS FINITE DIFFERENCE SCHEME FOR THE RELUGA x - y - z MODEL DISCRETE-TIME FRACTIONAL POWER DAMPED OSCILLATOREXACT FINITE DIFFERENCE REPRESENTATION OF THE MICHAELIS-MENTON EQUATION DISCRETE DUFFING EQUATION DISCRETE HAMILTONIAN SYSTEMS ASYMPTOTICS OF SCHRODINGER-TYPE DIFFERENCE EQUATIONS BLACK-SCHOLES EQUATIONS Appendix: Useful Mathematical Relations Bibliography Indexshow more