solving ODE that consists of erfc(x)

[sjung-2]

Dear all,

I'm trying to solve a PDE that consists of erfc(x) and exp(x^2) like the file attached below, which is simply a poisson's equation.

Since it has an unknown boundary condition, F electric field at position x=0, I tried 'minerr(F)' type resolution with F declared beforehand by initial guess.

Unfortunatlely, it keeps saying that F in the 'miners' syntax has not been defined.

Could anyone can help me?

Thank you in advance for your help.

Sung

[Werner_E · Accepted solution]

You have a unit problem/inconsistency which makes the odesolve solve block fail, when called. Furthermore you should change the label of F in V(F):=... to "variable".

The meter in constant A should be to the power of 2, not to the power of 5, as they are now. Otherwise you can't add F^2 (under the root).

I am not sure what the error is, you made, but if I boldly add the required units to A

your sheet works OK:

WE

[sjung-2]

Dear Werner,

It is my pleasure to have you again for this problem. I tried your tip and it works well.

In fact, I forgot to multiply N_{V} to the coefficient A that has a unit of m^{-3}.

Thank you very much for your keen observation.

Sungyeop

[sjung-2]

Dear Werner,

It seems solver work fine but, now, the problem is the value of V(d) which is unreasonably larger than 0.6 V (the boundary condition).

How can we make sure the boundary condition is fulfilled V(d) = 0.06 V, V(0) = 0?

Regards,

[Werner_E]

You may want to have a look at your ODE as it seems that F has not much influence on the outcome:

[sjung-2]

What an inspring comment it was. I made a mistake in the polarity of the coefficients. Converting signs of A, B, C resulted in a good results.

Thank you very  much Werner.

Sincerely,

Sungyeop