Interesting catalog of methods for numerical methods for ODEs

10222019, 03:55 PM
Post: #1




Interesting catalog of methods for numerical methods for ODEs
The following article has an interesting catalog of numerical methods for solving ordinary differential equations.
"DIFFERENTIAL EQUATION SOLVER SIMULATOR FOR RUNGEKUTTA METHODS by Metin HATUN & Fahri VATANSEVER" Enjoy! Namir 

10232019, 12:53 AM
Post: #2




RE: Interesting catalog of methods for numerical methods for ODEs
(10222019 03:55 PM)Namir Wrote: The following article has an interesting catalog of numerical methods for solving ordinary differential equations. Do you have a link to the article? Bob Prosperi 

10232019, 01:49 AM
Post: #3




RE: Interesting catalog of methods for numerical methods for ODEs
(10232019 12:53 AM)rprosperi Wrote:(10222019 03:55 PM)Namir Wrote: The following article has an interesting catalog of numerical methods for solving ordinary differential equations. El articulo de marras Regards, Bob. V. All My Articles & other Materials here: Valentin Albillo's HP Collection 

10232019, 02:00 PM
Post: #4




RE: Interesting catalog of methods for numerical methods for ODEs
(10232019 01:49 AM)Valentin Albillo Wrote: El articulo de marras 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. Bob Prosperi 

10232019, 09:11 PM
Post: #5




RE: Interesting catalog of methods for numerical methods for ODEs
Hi Namir,
thank you for this catalog ! Here is a link to programs I've just written to solve ODEs with a 10thorder RungeKutta method: http://hp41programs.yolasite.com/rk10.php Though these programs are slow with a real HP41, the precision is often very good. Best regards, JeanMarc. 

10232019, 10:19 PM
Post: #6




RE: Interesting catalog of methods for numerical methods for ODEs
Hi, Bob: (10232019 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 wellknown, widelyused 4^{th}order RungeKutta method you don't need that much power (71B+Math ROM), a cute HP25 will suffice, as demonstrated in my article: Long Live the HP25 ! which includes a 39step 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 HPcalc site ! Best regards. V. All My Articles & other Materials here: Valentin Albillo's HP Collection 

10252019, 03:29 AM
(This post was last modified: 10252019 02:50 PM by Namir.)
Post: #7




RE: Interesting catalog of methods for numerical methods for ODEs
(10232019 09:11 PM)JMBaillard Wrote: Hi Namir, Coding a 10th order RungeKutta on an HP41C is a very impressive task!! My hats off for you JeanMarc!! You are one of brilliant math/programmers for the HP41C. Namir 

10252019, 02:52 PM
Post: #8




RE: Interesting catalog of methods for numerical methods for ODEs
(10232019 09:11 PM)JMBaillard Wrote: Hi Namir, What computer programming languages do you use for the PC or mainframe? Which one is your favorite? Namir 

10252019, 07:19 PM
Post: #9




RE: Interesting catalog of methods for numerical methods for ODEs
Thank you for your appreciation, Namir !
I'm also writing programs that use 10thorder RungeKuttaNystrom 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. 

11042019, 04:11 AM
Post: #10




RE: Interesting catalog of methods for numerical methods for ODEs
(10232019 09:11 PM)JMBaillard Wrote: Here is a link to programs I've just written to solve ODEs with a 10thorder RungeKutta method: Following your link I've seen that you're using a 17stage (k1, k2, ..., k17) RK10 method needing 169 constants in all. I'm curious: Why haven't you used instead a 16stage 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. All My Articles & other Materials here: Valentin Albillo's HP Collection 

11062019, 04:04 PM
Post: #11




RE: Interesting catalog of methods for numerical methods for ODEs
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 FairyMary Goldilocks 

11062019, 05:27 PM
Post: #12




RE: Interesting catalog of methods for numerical methods for ODEs
The main point of highorder RungeKutta methods is to bootstrap high order predictorcorrect methods. It's not particularly hard to derive a PC method with high order. How PC methods are not selfstarting. RK methods of the same order the PC being used can start the PC without losing precision.


11062019, 11:23 PM
Post: #13




RE: Interesting catalog of methods for numerical methods for ODEs
(11042019 04:11 AM)Valentin Albillo Wrote:(10232019 09:11 PM)JMBaillard Wrote: Here is a link to programs I've just written to solve ODEs with a 10thorder RungeKutta method: Thank you for the info Valentin ! I didn't know this 16stage RK10 method before, and I'll try to use it in new programs. Best regards, JM. 

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