solving a system of equations involving numerical integration
- To: mathgroup at smc.vnet.net
- Subject: [mg42565] solving a system of equations involving numerical integration
- From: Vladimira A Ilieva <ilieva at U.Arizona.EDU>
- Date: Wed, 16 Jul 2003 09:13:29 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Could someone help me with the following code? I am trying to solve a
system of two equations in two unknowns which involve evaluation of
numerical integrals.
Clear[f];
Clear[g];
Clear[a];
Clear[b];
f[a_?NumericQ, b_?NumericQ] /; a != 0 || b != 0 := NIntegrate[1/(100 +
5*x + 5*y)^0.5*((1/(2*[Pi]* y))*((E^((-((Log[x] - Log[a] - 0.08)^2/2)) -
((Log[y] - Log[b] - 0.02)^2/2)))), {x,0.001, [Infinity]}, {y, 0.001,
[Infinity]}];
g[a_?NumericQ, b_NumericQ] /; a != 0 || b != 0 := NIntegrate[1/(100 + 5*x
+ 5*y)^0.5*((1/(2*[Pi]*x))*((E^((-((Log[x] - Log[a] - 0.03)^2/2)) -
((Log[y] - Log[b] -0.02)^2/2)))), {x, 0.001, [Infinity]}, {y, 0.001,
[Infinity]}];
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}]
Unfortunately, I get the following error message
FindRoot::"nlnum"), "The function value (-0.5686685479617104`, - 9.9636840576164
38`) is not a list of numbers with dimensions {2} at {a, b} = {1.`, 1.`}General
::nlnum
I would greatly appreciate any help!
Sincerely, Vladimira