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Thread: predictor-corrector scheme

  1. #1
    nad is offline
    Mar 2011

    predictor-corrector scheme

    I'm asking for help to understand the realization of the iterative predictor-corrector scheme (I'm not a specialist in this field) for PDE system . The description of a method attached in article.
    The question concerns algorithm realization under the formula (A5), resulted in article
    $\displaystyle U_i^{new}=U_i^{old}+dtF_i(\overline{U^{old}},\over line{U^{new}})$ (A5)
    where $\displaystyle F_i$ - function in the right part of the equations, and $\displaystyle \overline{U_i}$ - variables.
    , $\displaystyle U_i^{new}$ as I have understood, these are predicted value of all variables from, for example, Euler's method. Then it is necessary to calculate variables and to compare them with predicted, repeating algorithm before achievement of necessary accuracy. But how to calculate if in the right part there are the same $\displaystyle U_i^{new}$, for me not clearly? In any way I don't understand the dependence $\displaystyle F_i(\overline{U^{old}},\overline{U^{new}})$ of two variables means? How to use this formula in calculations? I will be glad to any concrete algorithms or the references to it.
    Wait for your suggestions.
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