MediumCalculusca-267

RK4 One Step

Problem

Take one classical fourth-order Runge-Kutta step for the ODE y' = t + y starting at (t, y) with step size h.

The stage slopes are k1 = f(t, y), k2 = f(t + h/2, y + h*k1/2), k3 = f(t + h/2, y + h*k2/2), and k4 = f(t + h, y + h*k3). Return y + h*(k1 + 2*k2 + 2*k3 + k4)/6.

Hint

The weighted average of the four slopes has fourth-order accuracy.

Test cases

case 1

in: [0,1,0.1]

expected: 1.1103416666666668

case 2

in: [0,1,0.5]

expected: 1.796875

case 3

in: [1,0,0.2]

expected: 0.24280000000000004

case 4

in: [0,0,0]

expected: 0

Starter codePython

def rk4_step(t, y, h):
    # Your code here
    pass

4 test cases · run your code against them in the editor