The Solution of Second-Order Functional Difference Equations

This paper reviews analytical and numerical techniques for solving second-order functional difference equations. A periodic multiplier aside, solutions to these equations can be expressed as linear combinations of two linearly independent particular solutions. One of these solutions can often be found either analytically, by exploiting a known relationship between both solutions, or numerically, by solving a simple integral equation. Knowledge of one particular solution permits construction of the second by solving a first-order functional difference equation.