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Science Forum Index » Math - Symbolic Forum » A Riccati differential equation...
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 Posted: Mon May 05, 2008 11:37 pm |
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Guest
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Dear Newsgroup:
http://mathforum.org/kb/thread.jspa?threadID=1738753&tstart=0
As I have mentioned before once a polynomial is solved in a class, it
has variety of applications, such as solving Riccati.
The following is a Riccati differential equation where, M(t),N(t) and
R(t) are arbitrary functions derived from the polynomial of degree
110, posted before on this topic
I have its general solution, without any integrals present.
Start substituting variety of values to its functions to see what
Maple presents the solution (like M(t)=t+1,N(t)=1/
(t^2-1),R(t)=3*t^4,and many more).
I will enclose its Maple input on file t1.
This is a member of a class, so, I have thousands like this in each
class, depending on computer memory and speed.
In some cases many solutions of Maple in terms of integrals and
hypergeometric functions will be solved, simply because I have its
general solution (of DE).
Those who think that I have no new ideas! , behave, as if stupidity
were a virtue.
Normally they have been hired in variety of positions as intellectual
slaves to praise others.
Dr.M.Basti |
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| Posted: Tue May 06, 2008 1:34 pm |
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Dear Newsgroup:
I was wondering if someone solved the Riccati, in general , with Maple
or Mathematica?
My Maple 11 was still running even over one GB of Ram on memory.
(How about supercomputers?).
This is one of simple classes I have within my collection.
Any interesting inputs for the variables?
Dr.M.Basti |
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| Vladimir Bondarenko... |
| Posted: Tue May 06, 2008 4:16 pm |
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Well, this is high poetry...
Eating Spaghetti,
Solving Riccati...
On May 6, 6:05Â pm, YBM <ybm... at (no spam) nooos.fr> wrote:
Quote: Basti... at (no spam) aol.com a �crit :
Dear Newsgroup:
I was wondering if someone solved the Riccati, in general , with Maple
or Mathematica?
I didn't, but I once solved a algebraic system with Maxima while eating
Spaghetti. |
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| Mehran Basti... |
| Posted: Tue May 06, 2008 7:50 pm |
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Dear Newsgroup:
It was a question in sci. physics newsgroup whether methods are also applied to Riccati difference equations (not differential)?
The answer is positive, and indeed a Riccati differential equation will govern the Riccati difference equations (which has many applications).
For example if you consider a simple difference equation:
s1:=x(n+1)= 2*x(n) +3;
Then with rsolve(s1,x(n)); on Maple:
Maple will solve it(check the solution).
If now we parameterize n=t, we notice that x(t) will be a solution of a linear differential equation:
dx/dt= ln(2)*(x(t)+3);
Indeed we may assume the coefficients of some differential equations involved are periodic.
I have paid little attention on difference equations, but it is clear to me that Riccati differential equations or its satellite functions will govern the difference equations.
Dr.M.Basti |
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| YBM... |
| Posted: Tue May 06, 2008 8:05 pm |
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Guest
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Basti05b at (no spam) aol.com a écrit :
Quote: Dear Newsgroup:
I was wondering if someone solved the Riccati, in general , with Maple
or Mathematica?
I didn't, but I once solved a algebraic system with Maxima while eating
Spaghetti. |
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| Vladimir Bondarenko... |
| Posted: Thu May 08, 2008 4:39 am |
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