0
$\begingroup$

I'm solving some coupled PDEs (Eb1 and Ef1) and what I plot for Eb1 appears to be correct. However, for some reason, when I go to plot Ef1, I get nothing. MWE is below (beginning is constants and functions needed to solve PDEs, relevant part near end)

(*Constants needed*)
a = 8.2314*10^-7; omega = 3.0318*10^7; Do2 = 2*10^-9; po = 106;
ro = 235*10^-6; micron = 1*10^-6; qm = 10^-4;
mic = 1*10^-6; De = 5.5*10^-11; eo = 100; j = 0.12; kmn = 4.7;
kme = 2.1; con = (a*omega)/(6*Do2); rl = Sqrt[(6*Do2*po)/(omega*a)];

(*Functions needed*)
rn = Piecewise[{{0, ro <=  rl}, {ro*(0.5 - Cos[(ArcCos[1 - (2*rl*rl)/(ro^2)] - 2*Pi)/3]), ro  > rl}}];

p[r_] = Piecewise[{{po + con*(r^2 - ro^2 + 2*(rn^3)*(1/r - 1/ro)), r > rn} , {0 , r <= rn}}];

q[r_] = qm*((kme/(kme + p[r]))*(p[r]/(kmn + p[r]))  + (kmn/(kmn + p[r]))*j);

(*Equations defined*)
eqnDe = D[Ef1[r, t], t] - De*(D[Ef1[r, t], r, r] + (2/r)*(D[Ef1[r, t], r])) + q[r]*Ef1[r, t];

eqnBo = D[Eb1[r, t], t] - (Ef1[r, t])*q[r];

(*Solving equations*)
x = NDSolve[{eqnBo == 0, Eb1[r, 0] == 0, eqnDe == 0, Ef1[r, 0] == 0, Derivative[1, 0][Ef1][rn, t] == 0, Ef1[ro , t] == eo}, 
  Eb1, {r, rn, ro}, {t, 0, 14400}];

Then it's easy to plot Eb1 between rn and ro with this;

Plot[Eb1[r, 14400] /. x, {r, rn, ro}, PlotRange -> Automatic]

and I get this;

enter image description here

Yet when I try to flow Ef1 with a similar command I get absolutely nothing;

Plot[Ef1[r, 14400] /. x, {r, rn, ro}, PlotRange -> Automatic]

enter image description here

Similarly, I can't seem to evaluate Ef1 at a given value of $r$ or $t$ - any ideas what I'm doing wrong and why this is the case?

$\endgroup$
1
$\begingroup$

It seems that you're missing a solution of Ef1. Try

y = NDSolve[{eqnBo == 0, Eb1[r, 0] == 0, eqnDe == 0, Ef1[r, 0] == 0, 
Derivative[1, 0][Ef1][rn, t] == 0, Ef1[ro, t] == eo}, 
Ef1, {r, rn, ro}, {t, 0, 14400}];
Plot[Ef1[r, 14400] /. y, {r, rn, ro}, PlotRange -> Automatic]

enter image description here

$\endgroup$
  • 1
    $\begingroup$ Thank you sir! Works absolutely perfectly. $\endgroup$ – DRG Jul 7 '14 at 15:49
  • $\begingroup$ @DRG No problem:-). $\endgroup$ – Gregory Rut Jul 7 '14 at 15:51

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.