Consider the following Runge-Kutta tableau #1 2 1 Jsing (*) you can answer part (c) even...

  

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Consider the following Runge-Kutta tableau #1 2 1 Jsing (*) you can answer part (c) even if you were not able to show (b). a) Calculate the order of consistency of the method above. Is that an explicit or an implicit method? For which sort of application and which level of accuracy would you apply this method? b) Show that the Runge-Kutta method for the tableau given above can be (re-)written as h n(t + h) = n(t) + hf (t+ - hs (t + 1/1 n( + h) + n()) (+) 2' c) Calculate the stability function R(z) and the stability domain for this method. Which type of stability does the method have? II Consider the following Runge-Kutta tableau #1 2 1 Jsing (*) you can answer part (c) even if you were not able to show (b). a) Calculate the order of consistency of the method above. Is that an explicit or an implicit method? For which sort of application and which level of accuracy would you apply this method? b) Show that the Runge-Kutta method for the tableau given above can be (re-)written as h n(t + h) = n(t) + hf (t+ - hs (t + 1/1 n( + h) + n()) (+) 2' c) Calculate the stability function R(z) and the stability domain for this method. Which type of stability does the method have? II