Hi,

i am solving a "duffing-like" 2nd order nonlinear diff. equation (in Matlab) 
using Dormand-Prince method (based on an explicit Runge-Kutta (4,5) formula) 
with variable step. However, how can i be sure that i have chosen a "good 
method", i.e. how can i examine the method, i.e. the errors of method used 
for solving of my equation?


Well, this question is not strictly Matlab-oriented so i posted it on 
math-group also.


Please, help!

Thanks. 

"pApAk" <noga@svinja.hr> wrote in message 
news:g1ghfr$l2p$1@news1.carnet.hr...
> Hi,
>
> i am solving a "duffing-like" 2nd order nonlinear diff. equation (in 
> Matlab) using Dormand-Prince method (based on an explicit Runge-Kutta 
> (4,5) formula) cut

Well, i have an additional question. Could anybody please explain me:

"based on an explicit Runge-Kutta (4,5) formula"

I know Runge-Kutta method but i dont know what is the meaning of "(4,5)" :-( 

"pApAk" <noga@svinja.hr> wrote in message 
<g1ghfr$l2p$1@news1.carnet.hr>...
> Hi,
> 
> i am solving a "duffing-like" 2nd order nonlinear diff. equation (in Matlab) 
> using Dormand-Prince method (based on an explicit Runge-Kutta (4,5) 
formula) 
> with variable step. However, how can i be sure that i have chosen a "good 
> method", i.e. how can i examine the method, i.e. the errors of method used 
> for solving of my equation?


This is why complete courses are provided
at the graduate level in numerical analysis, 
numerical linear algebra, numerical methods
for odes & pdes, etc. Your questions are
studied in depth in those courses.

John

In article <g1gikn$okj$1@news1.carnet.hr>, pApAk <noga@svinja.hr> wrote:

> "pApAk" <noga@svinja.hr> wrote in message 
> news:g1ghfr$l2p$1@news1.carnet.hr...
> > Hi,
> >
> > i am solving a "duffing-like" 2nd order nonlinear diff. equation (in 
> > Matlab) using Dormand-Prince method (based on an explicit Runge-Kutta 
> > (4,5) formula) cut
> 
> Well, i have an additional question. Could anybody please explain me:
> 
> "based on an explicit Runge-Kutta (4,5) formula"
> 
> I know Runge-Kutta method but i dont know what is the meaning of "(4,5)" :-( 
> 
> 
    a (4,5) RK is a fifth-order RK with an embedded 4th order method so
the results of each be used to estimate truncation error and
automatically adjust the stepsize taken.

pApAk wrote:

> Hi,
> 
> i am solving a "duffing-like" 2nd order nonlinear diff. equation (in Matlab) 
> using Dormand-Prince method (based on an explicit Runge-Kutta (4,5) formula) 
> with variable step. However, how can i be sure that i have chosen a "good 
> method", i.e. how can i examine the method, i.e. the errors of method used 
> for solving of my equation?
> 
> Well, this question is not strictly Matlab-oriented so i posted it on 
> math-group also.
> 
> Please, help!
> 
> Thanks. 

'sci.math.num-analysis' would be a good place as well.

Han de Bruijn

"Han de Bruijn" <Han.deBruijn@DTO.TUDelft.NL> wrote in message 
news:e3f4f$483be7fc$82a1e228$14547@news1.tudelft.nl...
> pApAk wrote:
>
>> Hi,
>>
>> i am solving a "duffing-like" 2nd order nonlinear diff. equation (in 
>> Matlab) using Dormand-Prince method (based on an explicit Runge-Kutta 
>> (4,5) formula) with variable step. However, how can i be sure that i have 
>> chosen a "good method", i.e. how can i examine the method, i.e. the 
>> errors of method used for solving of my equation?
>>
>> Well, this question is not strictly Matlab-oriented so i posted it on 
>> math-group also.
>>
>> Please, help!
>>
>> Thanks.
>
> 'sci.math.num-analysis' would be a good place as well.
>
> Han de Bruijn
>

Thanks for the advice. 

"John D'Errico" <woodchips@rochester.rr.com> wrote in message 
news:g1gn6l$up$1@fred.mathworks.com...
> "pApAk" <noga@svinja.hr> wrote in message
> <g1ghfr$l2p$1@news1.carnet.hr>...
>> Hi,
>>
>> i am solving a "duffing-like" 2nd order nonlinear diff. equation (in 
>> Matlab)
>> using Dormand-Prince method (based on an explicit Runge-Kutta (4,5)
> formula)
>> with variable step. However, how can i be sure that i have chosen a "good
>> method", i.e. how can i examine the method, i.e. the errors of method 
>> used
>> for solving of my equation?
>
>
> This is why complete courses are provided
> at the graduate level in numerical analysis,
> numerical linear algebra, numerical methods
> for odes & pdes, etc. Your questions are
> studied in depth in those courses.
>
> John

Well... Thanks :-/ 

"pApAk" <noga@svinja.hr> wrote in message 
<g1gulj$v1e$1@news1.carnet.hr>...
> "John D'Errico" <woodchips@rochester.rr.com> wrote in message 
> news:g1gn6l$up$1@fred.mathworks.com...
> > "pApAk" <noga@svinja.hr> wrote in message
> > <g1ghfr$l2p$1@news1.carnet.hr>...
> >> Hi,
> >>
> >> i am solving a "duffing-like" 2nd order nonlinear diff. equation (in 
> >> Matlab)
> >> using Dormand-Prince method (based on an explicit Runge-Kutta (4,5)
> > formula)
> >> with variable step. However, how can i be sure that i have chosen a 
"good
> >> method", i.e. how can i examine the method, i.e. the errors of method 
> >> used
> >> for solving of my equation?
> >
> >
> > This is why complete courses are provided
> > at the graduate level in numerical analysis,
> > numerical linear algebra, numerical methods
> > for odes & pdes, etc. Your questions are
> > studied in depth in those courses.
> >
> > John
> 
> Well... Thanks :-/ 

Did you expect me to write a complete,
full length book on the subject? There are
complete books on exactly these questions.
There are courses that go deeply into it.
Did you expect a two line answer that
would have resolved all of your questions?

I'm sorry, but not all of the questions one
might ask are answered by the number 42.

John

"John D'Errico" <woodchips@rochester.rr.com> wrote in message 
news:g1h0d1$fa9$1@fred.mathworks.com...
> "pApAk" <noga@svinja.hr> wrote in message
> <g1gulj$v1e$1@news1.carnet.hr>...
>> "John D'Errico" <woodchips@rochester.rr.com> wrote in message
>> news:g1gn6l$up$1@fred.mathworks.com...
>> > "pApAk" <noga@svinja.hr> wrote in message
>> > <g1ghfr$l2p$1@news1.carnet.hr>...
>> >> Hi,
>> >>
>> >> i am solving a "duffing-like" 2nd order nonlinear diff. equation (in
>> >> Matlab)
>> >> using Dormand-Prince method (based on an explicit Runge-Kutta (4,5)
>> > formula)
>> >> with variable step. However, how can i be sure that i have chosen a
> "good
>> >> method", i.e. how can i examine the method, i.e. the errors of method
>> >> used
>> >> for solving of my equation?
>> >
>> >
>> > This is why complete courses are provided
>> > at the graduate level in numerical analysis,
>> > numerical linear algebra, numerical methods
>> > for odes & pdes, etc. Your questions are
>> > studied in depth in those courses.
>> >
>> > John
>>
>> Well... Thanks :-/
>
> Did you expect me to write a complete,
> full length book on the subject? There are
> complete books on exactly these questions.
> There are courses that go deeply into it.
> Did you expect a two line answer that
> would have resolved all of your questions?
>
> I'm sorry, but not all of the questions one
> might ask are answered by the number 42.
>

I said "Thanks". I didnt have any expectations. However, courses and books 
are not available to everyone and, for instance, short explanation, a 
meaningfull advice or links would be more helpful than your answer.

But "Thanks" anyway.

However, do you maybe know what is the answer to life, the universe and 
everything?
;-)