Integrate and Solve
- To: mathgroup at smc.vnet.net
- Subject: [mg9723] Integrate and Solve
- From: Ed Hall <teh1m at holmes.acc.virginia.edu>
- Date: Tue, 25 Nov 1997 00:06:18 -0500
- Organization: uva
- Sender: owner-wri-mathgroup at wolfram.com
Folks,
I was hoping someone might have some insight into the reasons for the
following error messages I receiving using the Integrate and Solve
commands. I sent these questions to Wolfram Technical Support some
time ago but have not received a reply.
------------------------------------------------------------- The first
problem involves the following integral.
P=R*T/(V/m-b)-a/((V/m)^2+2*b*V/m-b^2);
Z=P*V/(m*R*T);
F=Integrate[(Z-1)*m/V,{V,0.1,Infinity}];
I get the error message,
In[5]:= F=Integrate[(Z-1)*m/V,{V,0.1,Infinity}]
Integrate::gener: Unable to check convergence
0.0707107
0.707107 a ArcTanh[0.707107 + ---------]
b m
Out[5]= -(m (2.30259 + ---------------------------------------- +
b R T
> 1. Log[0.1 - b m])) -
1
a m Pi Sign[b] Sqrt[-(-----------------)] Sign[m]
2 2
Sign[b] Sign[m]
> -------------------------------------------------
2 Sqrt[2] b R T
although when the upper limit is any real number, no error is
generated, e.g.
In[4]:= F=Integrate[(Z-1)*m/V,{V,0.1, 1.0 10^40}]
0.0707107
0.707107 a ArcTanh[0.707107 + ---------]
b m
Out[4]= -(m (2.30259 + ---------------------------------------- +
b R T
> 1. Log[0.1 - b m])) +
39
7.07107 10
0.707107 a ArcTanh[0.707107 + ------------]
b m
> m (-92.1034 + ------------------------------------------- +
b R T
40
> 1. Log[1. 10 - b m])
What are the general conditions under which the failure to test
convergence message is generated for the Integrate function?
-------------------------------------------------------------
The second problem involves the Solve function in the following way.
In[12]:= g1=2.0;
In[13]:= g2=2.0;
In[14]:= x1=2.0;
In[15]:=
Solve[{Log[g1]==-Log[x1+A*(1-x1)]+(1-x1)*(A/(x1+A*(1-x1))-B/(B*x1+(1-x1))),Log[g
2]==-Log[1-x1+B*x1]-x1*(A/(x1+A*(1-x1))-B/(B*x1+(1-x1)))},{A,B}]
-2. B
Solve::dinv: The expression (2. - 1. A)
involves unknowns in more than one argument, so inverse functions cannot
be used.
A B
Out[15]= Solve[{0.693147 == -1. (--------- - ----------) - Log[2. - 1. A],
2. - 1. A -1. + 2. B
A B
> Log[2 g] == -2. (--------- - ----------) - Log[-1. + 2. B]}, {A, B}]
2. - 1. A -1. + 2. B
Do you have any suggestions on how I might solve this pair of equations?
---------------------------------------------------------------------
Thanks in advance for any help.
Ed
--
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Ed Hall Research Computing Support
edhall at virginia.edu Information Technology and Communication
804-924-0620 The University Virginia