1. A-stability Recall from the lecture that the region of A-stability is defined by DA = {z EC: 14(2)| < 1}, where yn+1
Posted: Sat Feb 26, 2022 11:20 am
- 1 A Stability Recall From The Lecture That The Region Of A Stability Is Defined By Da Z Ec 14 2 1 Where Yn 1 1 (39.32 KiB) Viewed 45 times
1. A-stability Recall from the lecture that the region of A-stability is defined by DA = {z EC: 14(2)| < 1}, where yn+1 = PlhX)yn is the numerical solution of the ODE y' = dy. Compute 4(2) for the classical Runge Kutta method (RK4) and plot the region of A- stability with Python. Hint: Plot the function 1 14(x+iy) <1 o else f(x,y)={ with the command contourf. Hint: With our definition of the Runge K method, it is easier to compute hk; instead of ki. This ensures that we can combine hd =: 2 throughout the entire calculation.