I need to solve this using iteration method

y <t> = 0.8 y <t-1> +1

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- Apr 11th 2009, 10:44 AMmolimoliFirst order difference equation
I need to solve this using iteration method

y <t> = 0.8 y <t-1> +1 - Apr 11th 2009, 02:11 PMSoroban
Hello, molimoli!

Is there any more information . . . like the first term?

Quote:

I need to solve this using iteration method: .

. . I'll change the notation to a more convenient form (for me).

We have: .

We conjecture that is an exponential function: .

Subtract [2] - [1]: .

Multiply by 5, divide by

Factor and solve: .

Hence, the function is of the form: .

Suppose the initial term is: .

. . Then: .

Then we have:

Subtact [3] - [4]: .

Substitute into [3]: .

Therefore: .

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In the original notation: .