Hi Naveen, have a look at this report from the RISC group,where they list the algebraic solutions of the kamke ODEs. Check if there are cases that fall under case 1, or you can construct a solution yourself. Take the solution y(x) that belongs to case 1, select a couple of poles construct a solution and write it as a Riccati ode.
https://www3.risc.jku.at/publications/download/risc_5197/RISCReport15-19.pdf Also, try splitting the solver into a number of independent functions, like a function to determine poles, checking if a pole is really a pole, etc. Best, Nijso On Saturday, 27 March 2021 at 15:16:26 UTC+1 naveensai...@gmail.com wrote: > Hi Nijso, > > Are there any examples which walk through the entire algorithm? If so, > could you please link them here? I've written a pretty basic function which > should work for Case 1, but it doesn't. I could include the code for it too > if required. > > Naveen > On Thursday, March 25, 2021 at 10:36:37 AM UTC+5:30 Naveen Saisreenivas > Thota wrote: > >> I checked some examples of laurent series expansion and the series >> function seems to give correct results. Some examples I tested where from - >> >> 1. http://courses.washington.edu/ph227814/228/W14/notes/Laurent.nb.pdf >> 2. >> https://piazza.com/class_profile/get_resource/iw9kxycftxk6su/iy5oz4r144i6rr >> 3. >> https://www.maplesoft.com/support/help/Maple/view.aspx?path=numapprox/laurent >> >> Naveen >> On Thursday, March 25, 2021 at 9:27:47 AM UTC+5:30 Naveen Saisreenivas >> Thota wrote: >> >>> > Is the Laurent series actually needed? >>> >>> > I haven't read the paper but I looked at algorithm 11. Step 5 says >>> > "compute the poles of a(x) and their orders". Is it not just asking >>> > for the partial fraction expansion? >>> >>> I think Laurent Series is required in step 6 where we have to calculate >>> the coefficient vectors for each singular point. >>> >>> Naveen >>> On Wednesday, March 24, 2021 at 9:47:42 PM UTC+5:30 Oscar wrote: >>> >>>> On Tue, 23 Mar 2021 at 12:45, Naveen Saisreenivas Thota >>>> <naveensai...@gmail.com> wrote: >>>> > >>>> > I have some doubts regarding Algorithm 11. Please help me understand >>>> them - >>>> ... >>>> > >>>> > Lastly, finding the coefficient vectors requires Laurent Series >>>> expansion. I'm not sure if the series module can achieve this. There seems >>>> to be a function laurent_series, but I couldn't understand the >>>> documentation. Perhaps Oscar could help us out here. >>>> >>>> Is the Laurent series actually needed? >>>> >>>> I haven't read the paper but I looked at algorithm 11. Step 5 says >>>> "compute the poles of a(x) and their orders". Is it not just asking >>>> for the partial fraction expansion? >>>> >>>> Oscar >>>> >>> -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/c452bfd9-2d1a-42c7-a1db-39fe0f805fc4n%40googlegroups.com.
