COMPGROUPS.NET | Search | Post Question | Groups | Stream | About | Register

### How to choose a numerical method?

• Email
• Follow

```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.

Thanks.

```
 0
Reply noga1 (5) 5/27/2008 8:40:04 AM

See related articles to this posting

```"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

"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)" :-(

```
 0
Reply noga1 (5) 5/27/2008 8:59:44 AM

```"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
```
 0
Reply woodchips (7942) 5/27/2008 10:19:01 AM

```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
```
 0
Reply cbarron413 (16) 5/27/2008 10:29:33 AM

```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.
>
>
> Thanks.

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

Han de Bruijn

```
 0
Reply Han.deBruijn (44) 5/27/2008 10:52:43 AM

```"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.
>>
>>
>> Thanks.
>
> 'sci.math.num-analysis' would be a good place as well.
>
> Han de Bruijn
>

```
 0
Reply noga1 (5) 5/27/2008 12:24:22 PM

```"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 :-/

```
 0
Reply noga1 (5) 5/27/2008 12:25:00 PM

```"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

John
```
 0
Reply woodchips (7942) 5/27/2008 12:56:01 PM

```"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
>

I said "Thanks". I didnt have any expectations. However, courses and books
are not available to everyone and, for instance, short explanation, a

But "Thanks" anyway.

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

```
 0
Reply noga1 (5) 5/27/2008 1:37:59 PM

8 Replies
39 Views

Similar Articles

11/30/2013 9:24:13 AM
page loaded in 131601 ms -0