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Example of a trapezoidal predictor-corrector method
In this example ''h'' = <math>\Delta{t} </math>, <math> t_{i+1} = t_{i} + \Delta{t} = t_{i} + h </math>
: <math> y' = f(t,y), \quad y(t_0) = y_0. </math>
first calculate an initial guess value <math>\tilde{y}_{g}</math> via Euler
: <math>\tilde{y}_{g} = y_i + h f(t_i,y_i)</math>
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If I remember correctly, the iterative process converges quadratically. Note that the overall error is unrelated to convergence in the algorithm but instead to the step size and the core method, which in this example is a trapezoidal, (linear) approximation of the actual function. The step size ''h'' ( <math>\Delta{t} </math> ) needs to be relatively small in order to get a good approximation. Also see [[stiff equation]]
[[User:Jeffareid|Jeffareid]] ([[User talk:Jeffareid|talk]])
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