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MathGroup Archive 1996

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Innacurate Solve results

  • To: mathgroup at smc.vnet.net
  • Subject: [mg4029] Innacurate Solve results
  • From: Mark Van de Vyver <mvyver at ecel.uwa.edu.au>
  • Date: Mon, 20 May 1996 02:15:02 -0400
  • Organization: Dept. Acc. and Fin., Uni. of Western Aust, Perth, 6907
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

I'm battling with Solve and the following problem.
The Problem is set up in mma as follows:

In[1]

Clear[ m, v, X0, ximageB, ximageC, A, imagestrength, q1, q] 
q1[x0_,x_,t_]:=(2 Pi t)^(-1/2) Exp[-(x-x0-m t)^2 (2 t v)^-1] 
a[t_]:=1/2 - t*Log[1/4 + (E^(-t^(-1)))^(1/2)/2^(1/2)] 
t=1;
m=0; 
v=1; 
X0=0; 
ximageB=1; 
ximageC=2; 
A=1; 
(* imagestrength=1/2; *) 

In[2]

Solve[ {q[x, t]==A q1[X0, x, t] + imagestrength q1[ximageB, x, t] + imagestrength q1[ximageC, x, t], 
       A q1[X0, x, 0] + imagestrength q1[ximageB, x, 0] + imagestrength q1[ximageC, x, 0]==DiracDelta[x], 
       A q1[X0, a[t], t] + imagestrength q1[ximageB, a[t], t] + imagestrength q1[ximageC, a[t], t]==0},
{ q[x,t], imagestrength}]//Simplify

The result mma gives is close but v. innacurate and v. messy. For example applying //N to imagestrength gives 
-0.44....
It should be -0.5.
Further more q[x,t] should be the same as
g[y_, t_]=( (2 Pi t)^(-1/2) ) (Exp[-(y^2)/(2t)]-(1/2) Exp[-((y-1)^2)/(2t)]-(1/2)Exp[-((y-2)^2)/(2t)])
Ploting q and g will make clear how large the problem is and that whatever mma is doing wrong grows as x does.

Can anyone point me the problem out to me, or where I might find a solution.
Thanks in advance

Mark
-- 
   Mark Van de Vyver
_____________________________________________________________________________
   Mark Van de Vyver
   Department of Accounting and Finance      Phone:  (61) (09) 380-2510      
   University of Western Australia           Fax:    (61) (09) 380-1047        
   Nedlands   6907                           e-mail: mvyver at ecel.uwa.edu.au 
   Perth
_____________________________________________________________________________

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