15. Apply the implicit Runge-Kutta method (5.69) to the model problem Y' = XY, t 0,...

Transcribed Image Text:

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. 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.

Answer rating: 100% (QA)

To describe the motion of the spool we can use a polar coordinate system with the origin at the cent... View the full answer