Hello all,

I was hoping to get some general tips for tackling numeric integrals. As someone with little experience in the subject, I find myself overwhelemed by the many different integration methods. 

Experts, what are the first steps you take when trying to find a numeric solution to an integral? How might you zero-in on a particular integration method? What about tweaking error parametrs, etc.? Is there a general framework for approaching these problems, or is it all guesswork?

Thanks!

Hello experts,

I am trying to use solve to find a solution to a system of two equations. The two equations involved are quite complicated, and so sometimes Maple has difficulty with this. In particular, the solve command tries evaluating but never comes up with a solution (I've waited at least an hour, before giving up). 

I recently learned about fsolve, which gives approximate numeric solutions (which would be fine for my purposes), but fsolve too struggles with a solution and simply returns my input to me. I tried plotting the system of equations using plots:-implictplot to see if a solution existed, and as expected it does. I was hoping to get some tips on trying to solve a difficult system like this, perhaps given the knowledge that a solution definitely exists. Unfortunately, I need a solution for many variations of the same system, so simply reading off the approximate solution isn't really an option.

In my attatched code, the system with W = 49 is the first one where Maple really begins to struggle, and I believe that solutions for W>49 are also difficult.

06042020_Predicting_w_AB_Ratio_Maple_Primes.mw

Thanks!

Hello.

With the Curvefitting[Spline] command I calculate a piecewise function from discrete points. I perform this action 250 times and save the piecewise functions into a matrix. The process takes quite a while. Is it possible to save said matrix to a file such that I may call it from other maple worksheets, instead of re-calculating the matrix every time I want to use it?

Thanks. 

Hey there.

I'm trying to fill out the entries of a matrix. Each matrix element is the result of a very complicated calculation. Currently, I am using nested do loops (two loops total) to scan through each row and column respectively. I find that this process racks up a ton of memory, and that I often run out of memory before the matrix has been completely specified (depending on how big a matrix I want).

First, why is this happening? And second, what is a smarter way to perform the calculation? I will attatch my code below.

Cheers!

MaplePrimes2MuchMemory.mw

I have a tough integral I'm trying to solve (see attatched code). Maple seems to be able to compute it if I instruct it to integrate by parts, however the solutions don't make sense. For example, if I differentiate the result I expect to get my original integrand, but I do not. Furthermore, depending on which function you choose as 'u' and which as 'dv' when integrating by parts yields different results.

071319_Integral.mw

The attatched code has four examples:

1) Definite integration by parts

2) Indefinite integration by parts

3) Indefinite integration by parts, alternate choice of 'u'

4) Definite integration by parts, alternate choice of 'u'

and after each indefinite integration, I differentiate the result to compare with the orginal integrand.

What is going on here?