Interesting catalog of methods for numerical methods for ODEs

[Namir]

The following article has an interesting catalog of numerical methods for solving ordinary differential equations.

"DIFFERENTIAL EQUATION SOLVER SIMULATOR FOR RUNGE-KUTTA METHODS by Metin HATUN & Fahri VATANSEVER"

Enjoy!

Namir

[rprosperi]

(10-22-2019 03:55 PM)Namir Wrote:  The following article has an interesting catalog of numerical methods for solving ordinary differential equations.

"DIFFERENTIAL EQUATION SOLVER SIMULATOR FOR RUNGE-KUTTA METHODS by Metin HATUN & Fahri VATANSEVER"

Enjoy!

Namir

Do you have a link to the article?

[Valentin Albillo]

(10-23-2019 12:53 AM)rprosperi Wrote:  

(10-22-2019 03:55 PM)Namir Wrote:  The following article has an interesting catalog of numerical methods for solving ordinary differential equations.

"DIFFERENTIAL EQUATION SOLVER SIMULATOR FOR RUNGE-KUTTA METHODS by Metin HATUN & Fahri VATANSEVER"

Do you have a link to the article?

El articulo de marras

Regards, Bob.
V.

[rprosperi]

(10-23-2019 01:49 AM)Valentin Albillo Wrote:  El articulo de marras

Regards, Bob.
V.

Thanks Valentin. RK was one of my earliest introductions to numerical methods programming (about 100 years ago...) so this topic caught my eye. After a quick glance at the article, it's clear I should have spent more of those 100 years working with said RK math in order to better appreciate the article, but perhaps a slower, more thorough reading will help. Back in the day, most of said programming was in Fortran, so it's naturally comfortable to use a 71B with Math ROM when dabbling with this stuff.

Thanks again, and to Namir for the post.

[JMBaillard]

Hi Namir,

thank you for this catalog !

Here is a link to programs I've just written to solve ODEs
with a 10th-order Runge-Kutta method:

http://hp41programs.yolasite.com/rk10.php

Though these programs are slow with a real HP41,
the precision is often very good.

Best regards,
Jean-Marc.

[Valentin Albillo]

 
Hi, Bob:

(10-23-2019 02:00 PM)rprosperi Wrote:  Thanks Valentin. RK was one of my earliest introductions to numerical methods programming [...] Back in the day, most of said programming was in Fortran, so it's naturally comfortable to use a 71B with Math ROM when dabbling with this stuff.

Well, at least for the well-known, widely-used 4^th-order Runge-Kutta method you don't need that much power (71B+Math ROM), a cute HP-25 will suffice, as demonstrated in my article:

          Long Live the HP-25 !

which includes a 39-step RPN program implementing it and still leaving 10 steps to define the y'=f(x,y) to be solved.

Now back to uploading the files for the update #003 to my HP-calc site !

Best regards.
V.

[Namir]

(10-23-2019 09:11 PM)JMBaillard Wrote:  Hi Namir,

thank you for this catalog !

Here is a link to programs I've just written to solve ODEs
with a 10th-order Runge-Kutta method:

http://hp41programs.yolasite.com/rk10.php

Though these programs are slow with a real HP41,
the precision is often very good.

Best regards,
Jean-Marc.

Coding a 10th order Runge-Kutta on an HP-41C is a very impressive task!! My hats off for you Jean-Marc!! You are one of brilliant math/programmers for the HP-41C.

Namir

[Namir]

(10-23-2019 09:11 PM)JMBaillard Wrote:  Hi Namir,

thank you for this catalog !

Here is a link to programs I've just written to solve ODEs
with a 10th-order Runge-Kutta method:

http://hp41programs.yolasite.com/rk10.php

Though these programs are slow with a real HP41,
the precision is often very good.

Best regards,
Jean-Marc.

What computer programming languages do you use for the PC or mainframe? Which one is your favorite?

Namir

[JMBaillard]

Thank you for your appreciation, Namir !

I'm also writing programs that use 10th-order Runge-Kutta-Nystrom formula.

However, I don't know any programming language for a PC !
HP41 RPN & HP48 RPL are the unique programming languages that I know.
( my favorite one remains HP41 RPN )

Best regards.

[Valentin Albillo]

(10-23-2019 09:11 PM)JMBaillard Wrote:  Here is a link to programs I've just written to solve ODEs with a 10th-order Runge-Kutta method:

http://hp41programs.yolasite.com/rk10.php

Following your link I've seen that you're using a 17-stage (k1, k2, ..., k17) RK10 method needing 169 constants in all.

I'm curious: Why haven't you used instead a 16-stage RK10 method ? (same order but only 136 constants in all)

It would run significantly faster (1 stage less and fewer constants as well), would use less memory registers (33 data registers would be saved, as well as many program registers while initializing the constants) and the precision would be about the same or better.

V.

[Csaba Tizedes]

I scrolled down the article and I saw how the order of RK is higher and higher and grows and huge and grabs my shirt and bites my head off and I hoped I will found a "good enough order RK method" at the bottom, but I found nothing and it is maybe really important and really useful, but I lost what is the point of this...

Csaba - Hand by hand with the Fairy-Mary Goldilocks

[ttw]

The main point of high-order Runge-Kutta methods is to bootstrap high order predictor-correct methods. It's not particularly hard to derive a PC method with high order. How PC methods are not self-starting. RK methods of the same order the PC being used can start the PC without losing precision.

[JMBaillard]

(11-04-2019 04:11 AM)Valentin Albillo Wrote:  

(10-23-2019 09:11 PM)JMBaillard Wrote:  Here is a link to programs I've just written to solve ODEs with a 10th-order Runge-Kutta method:

http://hp41programs.yolasite.com/rk10.php

Following your link I've seen that you're using a 17-stage (k1, k2, ..., k17) RK10 method needing 169 constants in all.

I'm curious: Why haven't you used instead a 16-stage RK10 method ? (same order but only 136 constants in all)

It would run significantly faster (1 stage less and fewer constants as well), would use less memory registers (33 data registers would be saved, as well as many program registers while initializing the constants) and the precision would be about the same or better.

V.

Thank you for the info Valentin !

I didn't know this 16-stage RK10 method before,
and I'll try to use it in new programs.

Best regards,
JM.