(f)

To estimate the number of steps needed to get the first significant digit of the solution, let's try 50 steps (dt=0.1):

>

> ptsE := Euler( MODEL, IC, DOMAIN, 50 );

> ptsE[51];

The last value is now negative (that's an improvement), but is nowhere close to having the correct first significant digit.

>

> ptsE := Euler( MODEL, IC, DOMAIN, 250 ):

> ptsE[251];

>

That's better, let's double the number of steps to 500 (dt=0.01):

> ptsE := Euler( MODEL, IC, DOMAIN, 500 ):

> ptsE[501];

>

That does it! (Actually, while 400 is not enough steps, anything larger than 401 will suffice.)

>

> ptsE := Euler( MODEL, IC, DOMAIN, 400 ):

> ptsE[401];

>

> ptsE := Euler( MODEL, IC, DOMAIN, 401 ):

> ptsE[402];

>

> ptsE := Euler( MODEL, IC, DOMAIN, 402 ):

> ptsE[403];

>