MaplePrimes - Newest Comments

simpler

dharr — Wed, 13 May 2026 03:50:22 Z

Here's a simpler way to find two of the solutions, and of course the general solution is easy to find.

special case

dharr — Tue, 12 May 2026 23:32:14 Z

@dharr I found a slightly different tan solution which only works for a special relationship between e0 and e2, so probably that is what is meant.

fp3.mw

no tan solution

dharr — Tue, 12 May 2026 19:16:19 Z

@salim-barzani OK, lets take epsilon=1 then I agree with Eq 3.7. I needed W because you can't integrate wrt a function in Maple, i.e. int(..., w(xi__1)) doesn't work.

But as I showed there is no way to transform F to F2, so the integral that gives the arctan result is invalid, and so Eq 3.13 is incorrect, so it will not satisfy the ode. You can perfom the integral with e2 and e0 in (just change the Int to int). The problem is then that you get xi__1 = f(w) but here and in general f(w) has multiple w in, so you cannot easily invert it to get w as a function of xi__1.

The solution to this is to solve the ode in Eq 3.7. dsolve will do this directly, or you could take the square root and integrate. Since you get a general solution it will work for arbitrary e2 and e0. If you want to then find cases that are real for various choices of e2 and e0 you can make assumptions that make the things under the square roots positive.

it is great but still remain

salim-barzani — Tue, 12 May 2026 16:53:17 Z

@dharr you did a great job is ok if your result is different from him that is no matter the idea must be like this that solution you get must be the solution of ode first eq(3.5) based on thus changing variable also that epsilon you can mentioned be one, that solution you get arctan(#) must be solution of eq(3.5) then replaced eq(3.1) must be solution of eq(1.3) which is pde , also he metion a table 2 after eq(3.11) which i update here , i am not good with this transformation eq(3.6) but when you get the solution the solution must satisfy and in eq(3.13) is a solution of eq(3.7) then he apply eq(3.6) to get function (u(xi)) then he substitute in eq(3.1) to get final answer of pde beside your coding is work so good but i am not familiar with some coding in replacement and why you replace w(xi) by W i am not sure about that quadratic using why he use that even is a special kind of analytical method which this is so different from other i am intrested so much if apply to get solution of pde as he mention it will be something very different also you can use your coding and even update the steps he did it

paper

if need any help let me know i am work on it but some replacment make a problem for me i can't handle it , also dont use equation of him like eq(3.7) as you suppose maybe he is wrong use yours

Details about the use of Maple in that book

rcorless — Tue, 12 May 2026 16:24:04 Z

I wrote a LinkedIn post about them

Important points: All code is available (MIT license) at my GitHub site

The index of Maple commands used in the book is Open Access at the SIAM bookstore site linked above. That index doesn't just tell you where in the book the commands were used, they are a pointer to which commands were useful; I am happy that SIAM made the index open access.

near enough

dharr — Tue, 12 May 2026 13:47:41 Z

@salim-barzani The paper seems to have several errors

fp2.mw