Thread: ODE Solved Using Euler Method

I get the feeling I'm making a mistake somewhere here since the error is extremely high

Problem: Compute by hand using the Euler Method given:




Attempt:

Euler Method: y_i+1= y_i + h*f(t_i,y_i) where h is the arbitrary step size which in this case will be 0.1
y_i = 0
h = 0.1
f(t_i,y_i) = f(0,1) = -100(1) + 1 = -99
y_i+1= 1 + (-99)(0.1) = -8.9

To calculate percent error, find the exact solution.
Solving the ODE yields:
y = 1/100 + 99/(100*e^100t)

Plugging in 0.1 for t yields approximately 0.01005 for the exact solution as opposed to -8.9 in the approximated solution

Originally Posted by spruancejr

Euler Method: y_i+1= y_i + h*f(t_i,y_i) where h is the arbitrary step size which in this case will be 0.1
y_i = 0
h = 0.1
f(t_i,y_i) = f(0,1) = -100(1) + 1 = -99
y_i+1= 1 + (-99)(0.1) = -8.9

In the 4th and 5th lines you've taken as 1 instead of 0.

Thanks!

I incorrectly entered the initial condition.