Group Abstract

Message Boards

WOLFRAM COMMUNITY

12.2K Views

5 Replies

5 Total Likes

View groups...

Follow this post

Share this post:

GROUPS:

Differential Algebraic Equation

Shivi Sv

Shivi Sv, DAV College

Posted 11 years ago

There is an error in solving the attached differential algebraic equation. Someone kindly suggest me how to remove the error. Attachments:

POSTED BY: Shivi Sv

5 Replies

Sort By:

Shivi Sv

Shivi Sv, DAV College

Posted 11 years ago

POSTED BY: Shivi Sv

Bill Simpson

Posted 11 years ago

Perhaps I have misunderstood some part of your attachement. If I replace your NDSolve and the plots that follow it with this f = First[f/.NDSolve[{f''[\[Xi]]-1/f[\[Xi]]^3+1/eo f[\[Xi]] phir[\[Xi]] 10^7==0, f[0]==1, f'[0]==0}, f,{\[Xi],0,1}]]; Plot[f[\[Xi]], {\[Xi], 0, 1}, AxesOrigin->{0,0}, PlotStyle->{Thickness[0.006]}, AxesLabel->{f}, PlotRange->All] Plot[eta[\[Xi]]-Abs[(\[Xi] Exp[b1[\[Xi]]] a1[\[Xi]] Sqrt[pi/2])/2Exp[b1[\[Xi]]^2/8] (Erf[Sqrt[2]\[Xi]+b1[\[Xi]]/ (2 Sqrt[2])]-Erf[Sqrt[2](\[Xi](1-\[Beta][\[Xi]])-\[Beta][\[Xi]]*tdash)+b1[\[Xi]]/(2 Sqrt[2])])], {\[Xi], 0, 1}, AxesOrigin->{0,0}, PlotStyle->{Thickness[0.006]}, AxesLabel->{\[Xi]}, PlotRange->All] then it seems to find the desired function f and it then uses that f to evaluate your next expression. I am concerned that in your attachment you seem to want that next expression to equal zero, but from the second plot that does not seem possible. If I have made some mistake and you can explain what that was then I will see if I can correct it.

Perhaps I have misunderstood some part of your attachement.

If I replace your NDSolve and the plots that follow it with this

f = First[f/.NDSolve[{f''[\[Xi]]-1/f[\[Xi]]^3+1/eo f[\[Xi]] phir[\[Xi]] 10^7==0, f[0]==1, f'[0]==0}, f,{\[Xi],0,1}]];
Plot[f[\[Xi]], {\[Xi], 0, 1}, AxesOrigin->{0,0}, PlotStyle->{Thickness[0.006]}, AxesLabel->{f}, PlotRange->All]
Plot[eta[\[Xi]]-Abs[(\[Xi] Exp[b1[\[Xi]]] a1[\[Xi]] Sqrt[pi/2])/2*Exp[b1[\[Xi]]^2/8] (Erf[Sqrt[2]*\[Xi]+b1[\[Xi]]/
   (2 Sqrt[2])]-Erf[Sqrt[2]*(\[Xi]*(1-\[Beta][\[Xi]])-\[Beta][\[Xi]]*tdash)+b1[\[Xi]]/(2 Sqrt[2])])], {\[Xi], 0, 1},
   AxesOrigin->{0,0}, PlotStyle->{Thickness[0.006]}, AxesLabel->{\[Xi]}, PlotRange->All]

then it seems to find the desired function f and it then uses that f to evaluate your next expression.

I am concerned that in your attachment you seem to want that next expression to equal zero, but from the second plot that does not seem possible.

If I have made some mistake and you can explain what that was then I will see if I can correct it.

POSTED BY: Bill Simpson

David Vasholz

David Vasholz, Johns Hopkins University

Posted 11 years ago

Hi, I have looked at your attachment. One of the equations you wish to solve has the form {-(1/f[z]^3) + 2.03742*10^7/((1/3 - 0.166597 (1 + 8.14968/f[z]^2)^3.)^2 (1 + 8.14968/f[z]^2) f[z]^3) + (f^\[Prime]\[Prime])[z]} == 0 The left hand side is a list and the right hand side is a number. Therefore, it is impossible for a solution to exist. There is a coding mistake somewhere.