Question: Consider the implicit Runge-Kutta method The first step is Backward Euler to determine an approximation to the value at the midpoint in time and the

Consider the implicit Runge-Kutta method

U* = U" +f(U*, t, + k/2), Un+1 = Un + kf

The first step is Backward Euler to determine an approximation to the value at the midpoint in time and the second step is the midpoint method using this value.

(a) Determine the order of accuracy of this method.

(b) Determine the stability region.

U* = U" +f(U*, t, + k/2), Un+1 = Un + kf (U*, tn + k/2). %3D

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