@acer Thank you very much

Best wishes

@acer Thanks very much for explaining in detail. 

@tomleslie I always have a problem extracting the coefficients of "diff" functions in the expression. I saw you used "op~" to extract the coefficients in chebyshev(exp(x),x). 
Is it possible to apply a simillar way to take the coeffiecients of the expression including "diff"? For example, let me assume the following expresstion:
eq:=2*ln(x)*diff(y(x),x,x)+2*x*diff(y(x),x)+sin(x)*x^2*y(x);
Now, the coefficeints of diff(y(x),x,x), diff(y(x),x), and y(x) are 2*ln(x), 2*x, and sin(x)*x^2, respectively. 
How can I extract the above coefficients by coding in such a way you used for chebyshev(exp(x),x) or any other way you know?
Thanks

@acer Thanks very much for consuming your time.
Would you please more tell about "specfunc" and its applications?
Best wishes

@tomleslie 

Thanks very much for presenting a simple way to solve my problem. I wish you more explain what "tuning" is and give me an example about.
Best wishes

@acer 

Thanks very much for your attention to my problem
The mentioned procedures, especially the last one, are excellent. I think that the last procedure could be employed by Maple as a built-in procedure to overcome the drawback of the construction of sub- and superscribed variables in 1-D math.

@mmcdara 
Thanks veru much

@dharr 
Thanks very much.
Can you define a procedure or module to combine the construction of the sub- and super-scripted variable and the "alias" command in order to simplify calling the mentioned variable in the code?

In this way, one can use the aforementioned procedure (module) to establish a sub-super-scripted variable and address it easily.

@Carl Love Thank you for your reply. I kindly ask you to send me an example of a numerical, ie. non-symbolic, solution of a set of equations in parallel through either ‘solve’ command with ‘numeric’ option or the ‘fsolve’ command. I want to take an idea to numerically solve equations in parallel with that example.

best wishes

@Carl Love 

Dear Carl,

As you said, the coding in Maple is not effective to write a program in shared-memory parallelism. To the best of my knowledge, the shared-memory parallelism is far more effective than an independent-memory one. On the other hand, Maple weakly treats shared-memory parallelism because of the essence of built-in serial programming. It is a major drawback for Maple, unfortunately.

@Carl Love
Dear Carl,
Thank you for your attention to me. I wish there is either an idea or an algorithm to solve the equations in parallel.
Generally, I think Maple is almost weak to convert built-in serial procedures into parallel ones. Unfortunately, many of the commands are not be able to automatically execute in parallel.
Best wishes 

@Carl Love 

Dear Carl,

If possible, please solve for me a set of algebraic equations by the ‘solve’ in parallel, as an example. I hope that I take an idea through your specimen to solve other equations.

Do you send me the solution of an arbitrary set of equations in parallel?

Bset wishes

@Carl Love

Dear Carl,
Thank you for your attention to my problem. I am not sure the mentioned equation, which I am now involving, can be solved even in serial!. However, the solution of either linear or nonlinear some equation(s) is a permanent challenge for me. It is very important for me to find a way to solve equation(s) in parallel because I almost involve a linear or nonlinear set of equations taking long running time in serial.
Can you help me to overcome the problem forever? 

Best wishes

@Carl Love 

Dear Carl,
Thanks very much for your refined comments on my summary which is itself useful and informative.

@Carl Love