@Glowing But did you get 100% CPU utilization during the CPU test? 

@Glowing Is it possible to reverse the effects of that voltage-lowering utility? If so, reverse it, at least temporarily, to see if it makes a difference. And check that BIOS also.

When, I run my computers at 100%, I can feel them get hot in 5-10 seconds. I don't see how this utility could stop your computer from getting hot without limiting its performance.

I suspect that the difference you saw between the trial and full versions of Maple 2019 is just a coincidence. Maybe it was just that your ambient air temperature was lower, or your computer was on a surface that allowed more airflow.

@mehdi jafari I was just suggesting that you look carefully at the results of the inner integral to get ideas on how to proceed. In the above you suppressed the output of the inner integral, so you may not have learned anything from it.

@kfli If I understand this correctly, at the end of a certain phase of multiprocessing you have some 3-dimensional Arrays. Then you want to turn each of these Arrays into a Vector by laying rows (or columns, or the 3rd dimension) end-to-end. Is that right? If that's all you want, it's trivial to accomplish with ArrayTools:-Alias, and there's no point in using multiprocessing for that phase. The re-indexing is done in the background, and there's no copying of data.

@digerdiga asked:

• So, but I do need to call randomize() before rand(0.0..1.0) in order for rand to give different random numbers?

If you want different random numbers, you should call randomize() once per session (a restart starts a new session). Don't call randomize for each random number; indeed, doing so virtually guarantees that the numbers won't be random because the clock doesn't change fast enough.

• Are the numbers by randomize pseudo-random or true random numbers?

A call to randomize() with no arguments sets the seed to a value based on the real-time clock (something like the number of milliseconds since 1970). Once a seed is set, the sequence of random numbers is fixed. They are pseudo-random. Only very special computers can generate true random numbers. They need to measure something in the physical world, such as cosmic rays or the position of the opaque liquid in a Lava Lamp.

Note that randomize() does not generate random numbers. Rather, it sets the seed so that rand (and other commands) will use a new sequence of random numbers.

@shkarah Those things are only meaningful if a specific value of eta is used. And what's the point of making R into a list of 4 values when you want it to vary continuously?

Make a into an exact rational, like 3/10. Then look at the results of just the symbolic inner integral:

int(f*exp(-x), x= 0..y + t, AllSolutions);

@Preben Alsholm I was wrong about the computations between exact rationals being done first, but I did not mean that when parentheses were used.

@shkarah 

1. You can't use fi as a variable name in Maple; it's a reserved word (i.e., one that has special syntactic meaning, kind of like a punctuation mark). So, change this name to something else, such as Fi.

4. Plot f vs R: Do you mean that you want a plot of 4 curves f vs eta for the 4 values of R given (like I did the 4 curves for different values of H)? If so, I need fixed values of H and alpha, so what should I use?

5. Same question.

Unfortunately, there's a bug in MaplePrimes regarding uploading .maple files. Can you make that a .zip file and upload again? Or if there's no data files, just upload the .mw.

@Glowing I have Windows 10 Home version 1903.

Maybe that "totally safe" utility turned off your hyperthreading?

@Glowing The examples of Christian Wolinski and Axel Vogt above show that it clearly makes a difference whether you use a decimal point. In particular, it changes the order that things are added. Floating-point addition is not associative. Operations between exact rationals get done first.

@tomleslie 

Tom,

What the OP is trying to achieve: My guess is that this is one of those ubiquitous ODE BVPs in nano-magneto fluid dynamics.  (We've been getting I guess about two such questions a week for years now.) It appears that the OP is trying solve it by the Homotopy Perturbation Method, which is a series solution approximation technique for BVPs. I am just guessing.

@Glowing My Resource Monitor (through Windows Task Manager) shows 97% - 100% processor utilization, and my cputime/realtime is about 6 with numcpus = 8. I have Intel Core i7 - 7700HQ @ 2.80 GHz.

I also just ran a similar test for another Question using Grid, and I got a ratio of 5.6. You can see in my Answer to "Grid Toolbox C Compile".

@erik10 Yes, sprintf can be used wherever the syntax expects a string. I used it because I wanted a consistent 3-character width (including the white space) for each number. Still, the width varies a small amount because times is not a fixed-width font.