Problem 2. (Runge-Kutta method - J) In this exercise we will study a Runge-Kutta method that is given by k₁ = f(tn, yn) h k2= ftn+ k₁ 3' Yn + 3 ½ 4 ) 1kg = 5 (1₁ + 3 / 1, 3 — — — 1 + kg) k3 | tn h, Yn k4= f (tn+h, yn + k₁ − k₂+ k3) Yn+1 = h : Yn + − (k₁ + 3k2 + 3k3 + k4) 8 a) Present the method in the form of a Butcher tableau. b) Decide the order of the method. c) Implement this method in Python. d) Verify the convergence order numerically. For this you can use the example problem y' = 2ty, y(0) = 1, which has the analytical solution y(t) = et², on the interval [0, 1].

Problem 2. (Runge-Kutta method - J) In this exercise we will study a Runge-Kutta method that is given by k₁ = f(tn, yn) h k2= ftn+ k₁ 3' Yn + 3 ½ 4 ) 1kg = 5 (1₁ + 3 / 1, 3 — — — 1 + kg) k3 | tn h, Yn k4= f (tn+h, yn + k₁ − k₂+ k3) Yn+1 = h : Yn + − (k₁ + 3k2 + 3k3 + k4) 8 a) Present the method in the form of a Butcher tableau. b) Decide the order of the method. c) Implement this method in Python. d) Verify the convergence order numerically. For this you can use the example problem y' = 2ty, y(0) = 1, which has the analytical solution y(t) = et², on the interval [0, 1].

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.CR: Chapter 11 Review

Problem 47CR

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