Ordinary Differential Equations (ODEs)

Numerical methods for solving initial value problems: Euler, Heun's, and Runge-Kutta

Initial Value Problem

y' = -2ty, \quad y(0) = 1, \quad t \in [0, 2]

Exact solution: $y(t) = e^{-t^2}$

Step size (h):

11 steps

Step 0 / 10

Exact (dashed) Euler Slope field

n	t_n	y_n (Euler)	y(t_n) (Exact)	Error
0	0.000	1.000000	1.000000	0.000e+0

Use Euler's method with $h = 0.5$ to approximate $y(1)$ for the IVP:

y' = y, \quad y(0) = 1

Hint: Compute y(0.5) first, then use it to find y(1).