# hw4 - ME 210B Homework 4 Due 1 Consider the Runge-Kutta...

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ME 210B Homework # 4 Due February 18, 2009 1. Consider the Runge-Kutta method deﬁned by 3 - 3 6 | 1 4 3 - 2 3 12 3+ 3 6 | 3+2 3 12 1 4 | 1 2 1 2 (a) (1 point) Write the formula which corresponds to this Runge- Kutta matrix (b) (2 points) Using the order conditions from the book, verify that the method is order 4 (Hint: read Section 4.3 very carefully, in- cluding the examples). 2. (3 points) Write the following in Runge-Kutta matrix form, and ﬁnd its order via Taylor expansion: y n + 2 3 = y n + h 3 [ f ( y n + 2 3 ) + f ( y n )] y n +1 = y n + h 4 [3 f ( y n + 2 3 ) + f ( y n )] 3. (3 points) It has been argued that displaying absolute stability regions
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## This note was uploaded on 07/08/2009 for the course ME 210B taught by Professor Linda during the Spring '09 term at UCSB.

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