No more memory available in Mathematica, Fit the parameters of system of differential equation
- by user1058051
I encountered a memory problem in Mathematica, when I tried to process my experimental data. It's a system of two differential equations and I need to find most suitable parameters. Unfortunately I am not a Pro in Mathematica, so the program used a lot of memory, when the parameter epsilon is more than 0.4. When it less than 0.4, the program work properly. The command 'historylength = 0' and attempts to reduce the Accuracy Goal and WorkingPrecision didn`t help. I can't use ' clear Cache ', because there isnt a circle. I'm trying to understand what mistakes I made, and how I may limit the memory usage. I have already bought extra-RAM, now its 4GB, and now I haven't free memory-slots in motherboard
Remove["Global`*"];
T=13200;
L = 0.085;
e = 0.41;
v = 0.000557197;
q = 0.1618;
C0 = 0.0256;
R = 0.00075;
data = {{L,600,0.141124587},{L,1200,0.254134509},{L,1800,0.342888644},
{L,2400,0.424476295},{L,3600,0.562844542},{L,4800,0.657111356},
{L,6000,0.75137817},{L,7200,0.815876516},{L,8430,0.879823594},
{L,9000,0.900771775},{L,13200,1}};
model[(De_)?NumberQ, (Kf_)?NumberQ, (Y_)?NumberQ] :=
model[De, Kf, Y] = yeld /.Last[Last[
NDSolve[{
v (Ci^(1,0))[z,t]+(Ci^(0,1))[z,t]==
-((3 (1-e) Kf (Ci[z,t]-C0))/
(R e (1-(R Kf (1-R/r[z,t]))/De))),
(r^(0,1))[z,t]==
(R^2 Kf (Ci[z,t]-C0))/
(q r[z,t]^2 (1-(R Kf (1-R/r[z,t]))/De)),
(yeld^(0,1))[z,t]==
Y*(v e Ci[z,t])/(L q (1-e)),
r[z,0]==R,
Ci[z,0]==0,
Ci[0,t]==0,
yeld[z,0]==0},
{r[z,t],Ci[z,t],yeld},{z,0,L},{t,0,T}]]]
fit = FindFit[data,
{model[De, Kf, Y][z, t],
{Y > 0.97, Y < 1.03, Kf > 10^-6, Kf < 10^-4, De > 10^-13, De < 10^-9}},
{{De,7*10^-13}, {Kf, 10^-5}, {Y, 1}},
{z, t}, Method -> NMinimize]
data = {{600,0.141124587},{1200,0.254134509},{1800,0.342888644},
{2400,0.424476295},{3600,0.562844542},{4800,0.657111356},
{6000,0.75137817},{7200,0.815876516},{8430,0.879823594},
{9000,0.900771775},{13200,1}};
YYY = model[
De /. fit[[1]],
Kf /. fit[[2]],
Y /. fit[[3]]];
Show[Plot[Evaluate[YYY[L,t]],{t,0,T},PlotRange->All],
ListPlot[data,PlotStyle->Directive[PointSize[Medium],Red]]]
the link on the .nb file
http://www.4shared.com/folder/249TSjlz/_online.html
