Re: NDSolve with arrays
- To: mathgroup at smc.vnet.net
- Subject: [mg89262] Re: NDSolve with arrays
- From: dh <dh at metrohm.ch>
- Date: Mon, 2 Jun 2008 04:30:56 -0400 (EDT)
- References: <g1m8ev$ia$1@smc.vnet.net> <g1tjkt$ki8$1@smc.vnet.net>
Hi Svend,
define the derivatives by:
deriv[j_Integer,x_?NumericQ,funvals_]:=funvals[[
If[IntegerPart[Sqrt[j^2+x^2]]>n,n,IntegerPart[Sqrt[j^2+x^2]]] ]];
and replace: D[funs[[j]][x],x]==funs[[x0]][x] by:
D[funs[[j]][x],x]== deriv[x0,x,Table[(funs[[i]])[x],{i,1,n}]]:
the whole code:
n=10;
funs=Table[Symbol["f"<>ToString[j]],{j,1,n}];
deriv[j_Integer,x_?NumericQ,funvals_]:=funvals[[
If[IntegerPart[Sqrt[j^2+x^2]]>n,n,IntegerPart[Sqrt[j^2+x^2]]] ]];
tes={Table[funs[[j]][1]->j^2,{j,1,n}]};
Do[eq1[j_]:={D[funs[[j]][x],x]==
deriv[x0,x,Table[(funs[[i]])[x],{i,1,n}]],funs[[j]][x0]==(funs[[j]][x0]/.tes[[x0]])};
eqs=Flatten[Table[eq1[j],{j,1,n}]];
AppendTo[tes,NDSolve[eqs,funs,{x,x0,x0+1}][[1]]];,{x0,1,10}];
res=Table[Piecewise@Table[{(funs[[i]]/.Transpose[Drop[tes,1]][[i,j]])[x],x<j+1},{j,1,n-1}],{i,1,10}];
Plot[res,{x,1,4}]
hope this helps, Daniel
Svend.Domdey at googlemail.com wrote:
> to be more precise,
> play[x_, j_] :=If[ IntegerPart[x^2+j^2]>n, n, IntegerPart[x^2+j^2]>n],
> i.e. the index on the rhs of my equation depends both on j and x.
> any suggestions?
> thanks
> svend
>
>
> On May 29, 2:44 pm, svend <dom... at tphys.uni-heidelberg.de> wrote:
>> hi all,
>> i want to solve a PDE by discretizing in one variable in an array and solv=
> e. the equations are of the following type:
>> n = 10;
>> x0 = 1;
>> x1 = 10;
>>
>> play[x_] := IntegerPart[x]
>>
>> eq1 := {D[f[j][x], x] == f[play[x]][x], f[j][x0] == j^2}
>>
>> eqs = Flatten[Table[eq1, {j, 1, n}]]
>> fun = Flatten[Table[f[j], {j, 1, n}]];
>> tes = NDSolve[eqs, fun, {x, x0, x1}][[1]];
>>
>> my problem is that the variable x, in which the equation is differential, =
> also appears on the rhs in the "index" of my array. mathematica does not eva=
> luate "play[x]" during NDSolve and just tells me that the rhs is not numeric=
> al. I tried "_NumericQ" and similar things but nothing seems. I would be ver=
> y happy if someone could tell me how to resolve this.
>> thanks
>> svend
>
>
--
Daniel Huber
Metrohm Ltd.
Oberdorfstr. 68
CH-9100 Herisau
Tel. +41 71 353 8585, Fax +41 71 353 8907
E-Mail:<mailto:dh at metrohm.com>
Internet:<http://www.metrohm.com>