Chapter 5: Difference Equations

The following sections are included:

• Genesis of Difference Equations

  • Square-Root Iteration

  • Integral Depending on Two Parameters

• Existence and Uniqueness Theorem

• The Fundamental Operators

  • The Δ Operator

  • The Shift Operator, E

  • Difference of Functions

  • The Operator Δ⁻¹

• Worked Problems Based on Section 5.3

  • Examples A

  • Example B

  • Example C

  • Examples D

• First-Order Linear Difference Equations

  • Example A

  • Example B

  • Example C

• General Linear Difference Equations

  • General Properties

  • Linearly Independent Functions

  • Fundamental Theorems for Homogeneous Equations

  • Inhomogeneous Equations

• Worked Examples

  • Example A

  • Example B

  • Example C

  • Example D

• Linear Difference Equations with Constant Coefficients

  • Homogeneous Equations

  • Inhomogeneous Equations

  • Worked Examples

• Nonlinear Difference Equations

  • Homogeneous Equations

  • Riccati Equations

  • Clairaut’s Equation

  • Miscellaneous Forms

• Worked Examples of Nonlinear Equations

  • Example A

  • Example B

  • Example C

  • Example D

  • Example E

• Two Applications

  • Chebyshev Polynomials

  • A Discrete Logistic Equation

• Comments and References

• Bibliography