@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.

@Rouben Rostamian  Doesn't the flexibility of the rope have something to do with it? I see no parameter for it.

It seems odd to me that the y-coordinate of the free end is constant. Is that correct?

@vv The command plots:-inequal can handle intersections, unions, and combinations thereof; although it's true that by  using the list/set syntax common to most plotting commands you'll just get an intersection. For a combination of intersections and unions, see the last example on the ?inequal help page.

@vv Yes, certainly it's hopeless for expressions containing user-defined numeric functions that don't control error.

@vv The part that I didn't understand (but now do) was why this doesn't work:

Digits:= 10: #Or just accept the default.
evalf[2](evalf[Digits](p2-p1));

The reason is that Digits = 2 inside the outer evalf.  But if Digits is copied to another variable, that variable won't be changed by the outer evalf.

I'm working on a method to ameliorate the catasthropic cancellation without requiring the user to figure out the number of digits required to do that.