Re: solving a system of equations involving numerical integration
- To: mathgroup at smc.vnet.net
- Subject: [mg42568] Re: solving a system of equations involving numerical integration
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Wed, 16 Jul 2003 09:13:31 -0400 (EDT)
- Organization: Universitaet Leipzig
- References: <bf097l$vr$1@smc.vnet.net>
- Reply-to: kuska at informatik.uni-leipzig.de
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
your code below include serious syntax errors.
It is a wonder, that it run at all.
However With[{NIntegrate[...},...]
is perfect nonsense. With[] is to define
a temporal symbolic constant for the body of the With[]
statement i.e.
With[{plotPnts=12},
Plot3D[Sin[x*y],{x,0,Pi},{y,0,Pi},PlotPoints->plotPnts]
]
Regards
Jens
Vladimira Ilieva wrote:
>
> I am trying to find the solution to a system of two equations in two
> unknowns. The difficulty comes from the fact that the two equations involve
> numerical integration.
>
>
>
> Could you please let me know what you think about the code above? I have
> been running this code for hours with no response from Mathematica yet.
>
>
>
> Thanks!
>
>
>
> Clear[f];
>
> Clear[g];
>
> Clear[a];
>
> Clear[b];
>
>
>
> f[a_?NumericQ, b_?NumericQ]:=
>
>
>
> With[{NIntegrate[(1/(100+5x+5y)^0.5)*[ExponenitalE]^(((Log[x] - Log[a] -
>
>
>
> 0.03)^2/2) - ((Log[y] - Log[b] - 0.02)^2/2))/(2*Pi*y) , {x, 0.001, ∞},
>
>
>
> {y, 0.001, ∞}, Method -> Trapezoidal, MinRecursion -> 3, MaxRecursion ->
>
>
>
> 10]} /; ! (a == 0) || ! (b == 0)];
>
>
>
>
>
> g[a_?NumericQ, b_NumericQ] :=
>
>
>
> With[{NIntegrate[(1/(100 + 5x + 5y)^0.5)*[ExponentialE]^(((Log[x] - Log[a] -
>
>
>
> 0.03)^2/2) - ((Log[y] - Log[b] - 0.02)^2/2))/(2*Pi*x), {x, 0.001, ∞}, {y,
>
>
>
> 0.001, ∞}, Method -> Trapezoidal, MinRecursion -> 3, MaxRecursion -> 10]}
> /;
>
>
>
> ! (a == 0) || ! (b == 0)];
>
>
>
>
>
> FindRoot[{a == 0.95*f[a, b]*(100 + 5*a + 5*b)^0.5 , b == 0.95*g[a, b]*(100 +
> 5*a + 5*b)^0.5}, {a, 1}, {b, 1}]
>
>