Solution consisting scheme (?)

Asked Nov 20 '13 at 00:23

Active Nov 26 '13 at 01:05

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I need to prove that this implicit and multisteps scheme is consistent or not: $$y_{k+1}=\frac{1}{8}[9y_k-y_{k-2}+3hf(x_{k+1},y_{k+1})+6hf(x_k,y_k)-3hf(x_{k-1},y_{ k-1}) ]$$

but I'm a little lost because this is a multistep method and I have no light to be displayed in this case.

$\textbf{Edit:}$

The scheme is for compute a solution of a initial value problem:

$$y'(x)=f(x,y(x)) \ \ \ x\in [a,b]$$ $$y(a)=\alpha$$

And one method is consistent if the global truncation error tends to zero as $h$ (step size) tends to zero.

Thank you for your suggestions.

edited Nov 26 '13 at 01:05

asked Nov 20 '13 at 00:23

Hiperion

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what $f(x,y)$ means? any function?what is $h$? – chenbai Nov 20 '13 at 06:35
@chenbai, $f$ is a function that satisfies the necessary conditions for applying the method, and $h$ is the step size. – Hiperion Nov 26 '13 at 01:08

Solution consisting scheme (?)

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