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10 Only Possible Solution of Affine Difference Equation

The ten possible types of solutions to affine difference equation Difference Equation Solutions are sorted in the table below.

No

Type of Solution

Cases

1.

Constant

Difference Equation Solutions

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* , Difference Equation Solutions

Difference Equation Solutions , Difference Equation Solutions

Difference Equation Solutions , Difference Equation Solutions

* , Difference Equation Solutions

Difference Equation Solutions , Difference Equation Solutions

2.

Linearly increasing without bound

Difference Equation Solutions

Difference Equation Solutions , Difference Equation Solutions

3.

Linearly decreasing without bound

Difference Equation Solutions

Difference Equation Solutions , Difference Equation Solutions

4.

Exponentially increasing without bound

Difference Equation Solutions

* , Difference Equation Solutions

5.

Exponentially decreasing without bound

Difference Equation Solutions

* , Difference Equation Solutions

6.

Exponentially increasing to a bound

Difference Equation Solutions

Difference Equation Solutions , Difference Equation Solutions

7.

Exponentially decreasing to a bound

Difference Equation Solutions

Difference Equation Solutions , Difference Equation Solutions

8.

Oscillating with constant amplitude

Difference Equation Solutions

* , Difference Equation Solutions

* , Difference Equation Solutions

9.

Oscillating with increasing amplitude

Difference Equation Solutions

* , Difference Equation Solutions

* , Difference Equation Solutions

10.

Oscillating with decreasing amplitude

Difference Equation Solutions

Difference Equation Solutions , Difference Equation Solutions

Difference Equation Solutions , Difference Equation Solutions


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Preferable reference for this tutorial is

Teknomo, Kardi (2015) Difference Equation Tutorial. http:\\people.revoledu.com\kardi\ tutorial\DifferenceEquation\