Question: 15. Apply the implicit Runge-Kutta method (5.69) to the model problem Y' = XY, t 0, Y(0) = 1. (a) Show that the solution
15. Apply the implicit Runge-Kutta method (5.69) to the model problem Y' = XY, t 0, Y(0) = 1. (a) Show that the solution can be written as yn = [R(Ah)]" with R(z) = 1+ 1 - (b) For any real z < 0 show that |R (z)| < 1. In fact, this bound is true for any complex z with Real (z) < 0, and this implies that the method is absolutely stable.
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