= = 1+y 4. This problems asks you to use both the Forward Euler and the Runge-Kutta method specified by 1+t the Butcher

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1 Y 4 This Problems Asks You To Use Both The Forward Euler And The Runge Kutta Method Specified By 1 T The Butcher 1 (87.2 KiB) Viewed 38 times

= = 1+y 4. This problems asks you to use both the Forward Euler and the Runge-Kutta method specified by 1+t the Butcher array below to estimate solutions to the IVP y' with y(1) = 2 and t e [1, 2]. Start by using both methods to estimate y(2) with h .5 and computing the error. Then select several values of h < 10-5 to provide estimations of y(1.001) and y(2) for each method. What choice of h that you computed optimizes the error for each method? How do the methods compare for each t value? = 0 1/3 1/3 2/3 -1/3 1 1 1 -1 1 1/8 3/8 3/8 1/8