@aa13 Post your actual code please. Not abbreviations with ....  The error message "; unexpected" usually just means that you failed to close parentheses or square brackets.

@aa13 Post your actual code please. Not abbreviations with ....  The error message "; unexpected" usually just means that you failed to close parentheses or square brackets.

@dongtian@jlu.edu.cn A finite field of integers? Is the modulus less than 2^64?

Roughly what size is A? Is A dense upper triangular? Roughly how big is n? Is everything in hardware floating point (a.k.a. "double precision")?

I can't duplicate your results. I downloaded your worksheet and ran it in M17-64 Standard Windows 8 and both derivatives worked as expected. I resave it an attached it to this. See if it works for you now.

Download derivative.mw

@mehdi_mech

The solution you got with dverk78 and relerr= 1 is not very meaningful. A relerr of 10^(-n) means about n digits of accuracy, so relerr= 1 is 0 digits of accuracy, which is no accuracy at all. Recall the definitions of absolute error and relative error:

absolute error = |true value - computed value|

relative error = absolute error / |true value|

I'd be very wary of ever setting relerr larger than 1e-4.

For the rosenbrock solution (stiff= true), you need to set maxfun higher than its default, or set it to 0, which means infinity. This may make the solution slow.

When using rkf45, ck45, or rosenbrock you may specify a different abserr for each of your 18 output variables.

@mehdi_mech Is your system still an initial value problem (IVP)? That is, does each equation contain at least one derivative? Then you should explore all of the alternative methods available in dsolve. From your previous posts, I think you've tried the default rkf45 and rosenbrock. But there's also two gear methods, eight lsode methods, and dverk78.

You should also try increasing the value of abserr (maybe you should try that first). The defaut value of 10^(-7) can take a very long time if the scale of the problem is >> 1. (For example, if a dependent variable is on the order of 10^6, then abserr= 1 might be appropriate.) See ?dsolve,numeric,IVP . Follow the links from the first paragraph of "Discussion" to the various methods. Read very carefully the section about abserr beginning in the third paragraph of "Discussion". If your dependent variables have substantially different scales from each other, then you may need to use the "list form" of abserr. Also read ?dsolve,numeric,Error_Control .

If all of the above fails, then I think that it is very unlikely that you'll be able to achieve anything with an ad hoc (self-written) method.

I don't understand how you got the 5.6.

If the function x(t) is not known, then how will you use B?

What is the datatype of the entries that are supposed to be floats? Are they strings? If you're not sure, extract one entry from the Vector, for example x:= V[1], and check its op(0,x) to find out. Also helpful is lprint(x).

@maple fan Unfortunately, just because a Maple property exists, it doesn't necessarily mean that any other commands use that property. Since there seems to be no other help page with MutallyExclusive, that's a clue that it is not used. However, it's possible that it is used somewhere. You can do the following with any property:

assume(a::MutuallyExclusive);

is(a::MutuallyExclusive);

                   true

A great many commands, maybe the majority, make no use at all of assumptions.

@fereydoon_shekofte 

So, you need to find a particular value in an RGB image, and it may occur several times. Approximately what size images are we talking about? 500 x 500? About how many times do you expect to find it (very roughly, order of magnitude)? Can the value be in any of the three color layers? Is the special value 1?

After you've found the indices that point to the particular value, you want to pair those indices with another list of values. Where does that second list of values come from?

And then you want to create a Matrix using those index-value pairs. What do you plan to do with that Matrix?

I am curious what Windows Task Manager says during those 40 seconds. Is the Disk Utilization or Network Utilization maxed?

I wonder what are the steps that led to the set of indices and the set of values. And I wonder what you plan on doing with the resulting set of equations. I suspect that you could be about to attempt something terribly inefficient that could be better handled with Matrices.

@OffshoreEngineer I assume from your dependent variable names that you are using cylindrical coordinates. How about trying to solve the BVP in Cartesian coordinates?