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Science Forum Index » Math - Numerical Analysis Forum » Verifying numerical solution of nonlinear solver
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| Guest |
 Posted: Tue Dec 12, 2006 8:43 am |
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I am trying to solve a system of nonlinear equations involving some
parameters using the NAG solver c05ncf. Under some conditions, I can
solve the problem analytically . When comparing the analytical
solution to the numerical one, I found the numerical solution behaves
like the analytical one for some range of parameters. But for other
values for the main parameters we got some results which are not
relative. So, is there any way to verify if the results obtained are
roots of the problem or not. By the way, I am using continuation to
proceed from one value of the parameter to another.
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| Helmut Jarausch |
| Posted: Tue Dec 12, 2006 10:26 am |
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Guest
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fai391@googlemail.com wrote:
Quote: I am trying to solve a system of nonlinear equations involving some
parameters using the NAG solver c05ncf. Under some conditions, I can
solve the problem analytically . When comparing the analytical
solution to the numerical one, I found the numerical solution behaves
like the analytical one for some range of parameters. But for other
values for the main parameters we got some results which are not
relative. So, is there any way to verify if the results obtained are
roots of the problem or not. By the way, I am using continuation to
proceed from one value of the parameter to another.
If you have solved f(x)=0 then you could check norm(f(x_star))
where x_star is the given approximation. Unless the Jacobian of f
near x_star is very ill-conditioned, a small norm indicates a good
approximation of a zero.
But, a nonlinear system might have several (many) solutions
and by continuation you normally don't get all of them.
So, comparison with one (of many) analytical solutions
is difficult if not impossible.
Furthermore, not all "mathematical solutions" are legal solution
of the underlying problem.
--
Helmut Jarausch
Lehrstuhl fuer Numerische Mathematik
RWTH - Aachen University
D 52056 Aachen, Germany |
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