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