Numerical Methods

9

Difference Equations

The concept of difference equations is useful in the study of electrical networks and to solve differential equations. In fact, the difference equation is the discrete counterpart of the differential equations. We shall note that the partial differential equations are first converted into difference equations and then solved by numerical methods.

9.1 DEFINITIONS AND EXAMPLES

Definition 9.1. A difference equation is an equation which involves an independent variable, a dependent variable, and the successive differences of the dependent variables.

For example,

 

Δy_{n + 1} + y_n = 2n²,              (9.1)

 

Δy _{n + 1} + Δ²y_{n − 1} = 2,           (9.2)

 

y _{n + 3} − 5Δy_n = 2ⁿ                (9.3)

are difference equations.

Since successive ...