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Subject: Re: Solving second order differential equations
Date: Thu, 25 Nov 2010 18:19:05 +0000 (UTC)
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"Sridatta Pasumarthy" <sridatta1988@gmail.com> wrote in message <icm404\$2pn\$1@fred.mathworks.com>...
> Hi,
> How do i solve four differential equations of second order involving many variables (numerically)?
> I have referred van der pol (non-stiff) example in Matlab, but it didn't help much because i couldn't
> figure a way to convert these to first order right away. Please help me find a solution.
>
> Problem Structure
> ----------------------------------
> w' = [k*f(z)] * y'
> w * x'' = c*g(z) * y'
> w * y'' = f(z) + g(z) * x' + j(z) * z'
> w * z'' = c*j(z) * y'
> 1-(1/sqrt(w))=x'^2 + y'^2 + z'^2
>
> x(0)=0, y(0)=0, z(0)=0, dx/dt(0)=0, dy/dt(0), dz/dt(0)=v
> c,k,v are constants.
> It also doesn't help that f,g,j are complicated exponential functions based upon z.
>
> I am supposed to plot 'dw/dz' vs 'z'
> ----------------------------------
>
> Thanks,
> Sridatta
- - - - - - - -
Hello again Sridatta.  You said "four differential equations" but I count five!  With only the four variables x, y, z, and w, that seems to be one too many equations to satisfy.

Think of it this way.  If w were being held fixed, the three middle equations involving x'', y'', and z'' would suffice for solving for x, y, and z.  Allowing w to vary according to the first equation would again constitute a solvable problem of four equations and four unknowns.  I see no reason why that fifth equation should then hold true.

How do you explain this?  I am assuming that the functions f, g, and j are all already determined and not unknown functions.

Roger Stafford
```