Declaring functions in NDSolve?

Question

I have a simple enough series of coupled ODES, which is relatively easy to solve. It looks something like this.

err = 0.05; jc = 2500; b = 0.7; k = 1; pt = 2; pf = 1; n = 3; 

sdp :=  pt + err*pf;
scp :=  pt + erri*pf;
sup :=  pt + err*pf + delt;

sdn :=    bd*n;
scn :=  bc*n;
sun :=   bu*n;

vp[t_] :=  (jc*b)/(x[t]*sdp + y[t]*scp + z[t]*sup );
vn[t_] :=  (jc*(1 - b))/(x[t]*sdn + y[t]*scn + z[t]*sun );

pd[t_] := vp[t]*sdp + vn[t]*sdn;
pc[t_] := vp[t]*scp + vn[t]*scn;
pu[t_] := vp[t]*sup + vn[t]*sun;


ad[t_] :=  (pd[t]*(x[t] + y[t] + z[t]))/(x[t]*pd[t] + y[t]*pc[t] + z[t]*pu[t]);
ac[t_] :=  (pc[t]*(x[t] + y[t] + z[t]))/(x[t]*pd[t] + y[t]*pc[t] + z[t]*pu[t]);
au[t_] :=  (pu[t]*(x[t] + y[t] + z[t]))/(x[t]*pd[t] + y[t]*pc[t] + z[t]*pu[t]);

Now, if I declare some other constants, it's easy to solve my equations:

   delt = 0.25; erri =  3*err; bd = 0.3; bc = 0.3; bu = 0.3;

eqns = {x'[t] == k*x[t]*(ad[t] - 1), y'[t] == k*y[t]*(ac[t] - 1), 
 z'[t] == k*z[t]*(au[t] - 1), x[0] == 1800, y[0] == 100, z[0] == 10};

fun1 = NDSolve[eqns, {x,y,z}, {t,0,10}];
Plot[Evaluate[x[t]/.fun1],{t,0,10}]

But what I really want to do is put $delt$, $erri$, $bd$, $bc$ and $bu$ inside the MANIPULATE environment. This works fine if I write all $x'$, $y'$ and $z'$ explicitly in terms of these variables but is messy and extremely long. So what I tried was something like this;

Manipulate[{Plot[Evaluate[x[t] /. NDSolve[eqns, {x, y, z}, {t, 0, 10}]], {t, 0, 10}], 
Plot[Evaluate[y[t] /. NDSolve[eqns, {x, y, z}, {t, 0, 10}]], {t, 0,10}],
Plot[Evaluate[z[t] /. NDSolve[eqns, {x, y, z}, {t, 0, 10}]], {t, 0, 10}]}, 
{{bd, 0, "bd variable"}, 0, 1}, {{erri, err, "erri variable"}, err, 1},
{{bc, 0, "bc variable"}, 0, 1}, {{bu, 0, "bu variable"}, 0, 
1}, {{delt, 0, "delt variable"}, 0, 5}]

Yet when I run this, I get a non-numerical value error. I think this is because the variables are not being explicitly considered from their parent equations, but I'm not sure how to enter this in so it works; I thought the SetDelay notation would work but apparently not. Anyone have any ideas on the syntax to make this work?

Please remove any unnecessary material and reduce your problem down to a minimal working example (e.g. remove definitions that you don't use in the problematic codes etc). — MarcoB, Feb 12 '16 at 15:20
As @MarcoB says, you should try to come up with a minimal example. Try to see if you can reproduce the problem in a simple case where there is only one differential equation with only one parameter that you would like to Manipulate. — march, Feb 12 '16 at 16:44
I don't think this will work. I suggest you read up on ParametricNDSolve, it may be better suited to this job. — LLlAMnYP, Feb 13 '16 at 12:31

score 2 · Answer 1 · answered Feb 13 '16 at 03:50

This is mentioned in the possible issues of document of Manipulate: Manipulate only "notices" explicit visible parameters. The easiest way I can think of to fix your code is to use With to make those parameters explicit:

Clear[bd, erri, bc, bu, delt]
eqns = {x'[t] == k*x[t]*(ad[t] - 1), y'[t] == k*y[t]*(ac[t] - 1), 
   z'[t] == k*z[t]*(au[t] - 1), x[0] == 1800, y[0] == 100, z[0] == 10};

With[{eqns = eqns}, 
 Manipulate[{Plot[Evaluate[x[t] /. NDSolve[eqns, {x, y, z}, {t, 0, 10}]], {t, 0, 10}], 
   Plot[Evaluate[y[t] /. NDSolve[eqns, {x, y, z}, {t, 0, 10}]], {t, 0, 10}], 
   Plot[Evaluate[z[t] /. NDSolve[eqns, {x, y, z}, {t, 0, 10}]], {t, 0, 10}]}, {{bd, 0.3, 
    "bd variable"}, 0, 1}, {{erri, 3 err, "erri variable"}, err, 
   1}, {{bc, 0.3, "bc variable"}, 0, 1}, {{bu, 0.3, "bu variable"}, 0, 
   1}, {{delt, 0.25, "delt variable"}, 0, 5}]]

Declaring functions in NDSolve?

1 Answers1