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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>




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