Re: NDSolve with arrays

*To*: mathgroup at smc.vnet.net*Subject*: [mg89232] Re: NDSolve with arrays*From*: dh <dh at metrohm.ch>*Date*: Sun, 1 Jun 2008 03:33:47 -0400 (EDT)*References*: <g1m8ev$ia$1@smc.vnet.net>

Hi Svend, Name the 10 functions you are looking for: f1..f10. Note that all 10 functions have the same derivatives. Further, from t=m to t=m+1, the derivative is fm[x]. We therefore solve the equations from t=1 to t=2 using f1 for the derivatives. Then from t=2 to t=3 using f2 etc. Therefore we have an outermost Do loop that iterates over starting times. To solve, we first setup a list with function names:funs = Table[Symbol["f" <> ToString[j]], {j, 1, n}] Then we define the equations, remembering that in step m the derivatives are given by fm: eq1[j_]:={D[funs[[j]][x],x]==funs[[x0]][x],funs[[j]][x0]==(funs[[j]][x0]/.tes[[x0]])}; eqs=Flatten[Table[eq1[j],{j,1,n}]]; finally we solve ad append the soulution to the solution list: tes: AppendTo[tes, NDSolve[eqs, funs, {x, x0, x0 + 1}][[1]]]; Finally we need to assemple the different pieces of the 10 functions into Piecewise functions: Table[Piecewise@Table[{(funs[[i]]/.Transpose[Drop[tes,1]][[i,j]])[x],x<j+1},{j,1,n-1}] ,{i,1,10}]; Here is the whole code: n=10; funs=Table[Symbol["f"<>ToString[j]],{j,1,n}]; tes={Table[funs[[j]][1]->j^2,{j,1,n}]}; Do[ eq1[j_]:={D[funs[[j]][x],x]==funs[[x0]][x],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 wrote: > hi all, > i want to solve a PDE by discretizing in one variable in an array and solve. 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 evaluate "play[x]" during NDSolve and just tells me that the rhs is not numerical. I tried "_NumericQ" and similar things but nothing seems. I would be very 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>