@Kitonum 

Indeed, this works, but unfortunatelly it is difficult to manage the plots by mouse.

@Preben Alsholm 

This situation in our languge is called "difficulties of translation" (I don't know, if there is a similar idiom in English). In item 1 I wished to say, that read operator does not read any content from *.m file: neither S1, no something else. But for any other extentsion it is possible to save and read to/from a file without problems. I used the term "returns" in wrong way.

Nevertheless, can you suggest any approach for the problem I described above:

Next, I see, that it is necessary to use output = array for correct saving of solution. But I have to calculate integrals on z(x) and z'(x); besides, the second derivatives of solution (z''(x)) are incorporated into right part of ODE, which I solve later. If z(x) and z'(x) are procedures, I can find z''(x) from initial ODE and fulfill all calculations, But if z(x) and z'(x) are presented by arrays, I should write special procedure for numerical integration of such functions (presented by a set of points). It is desirable to avoid this.

@Preben Alsholm 

Thank you for assistance, I hope, finally I will be able to solve a problem.

What do you mean about puzzling 1 and 2?

1. If S1 saved into external file with m extention (filename.m), it is not possible to read it by read operator. In other words, read returns nothing. Any other extention allows to save and read S1 as needed.

2. Assuming with subs indeed is more simple, now I use this workaround.

Clearly?

Next, I see, that it is necessary to use output = array for correct saving of solution. But I have to calculate integrals on z(x) and z'(x); besides, the second derivatives of solution (z''(x)) are incorporated into right part of ODE, which I solve later. If z(x) and z'(x) are procedures, I can find z''(x) from initial ODE and fulfill all calculations, But if z(x) and z'(x) are presented by arrays, I should write special procedure for numerical integration of such functions (presented by a set of points). It is desirable to avoid this.

BTW, I have the same configuration (M 18.02, W 7 x86 Ult).

@Preben Alsholm 

I could not reproduce some your steps. Maybe, the version of Maple or platform matter?

1. When I save the solution to *m file (Maple internal formft), read operator reads nothing from the file. Saving into a file with any other extension don't produce any issues (all works).
2. Syntax subs(S1,z(x)) is ideed simpler, I shall use it for further.
3. There is no problem with printing by showstat(`dsolve/numeric/hermite`) (as you metioned above). But assigning `dsolve/numeric/hermite`:=proc (................... doesn't solve the problem. After entering F1(0.12345)  the following error occurs: Error, (in F1) invalid input: diff received .13, which is not valid for its 2nd argument.

The cause is that the upper limit for variable y is not constant.

@acer 

Since 2D Output is a character style, I suppose, that alignment is defined by the following:

@Kitonum 

You are right, but for some reasons I would like to force Maple to work properly........

@Kitonum 

Thank you for advise, but, to my mind, the simplest way is the use of abacus istead of computer (it's a joke, don't be offended).

@ 

Thank you, now I'm aware of this approach.

@Carl Love 

Thank you, Carl. Indeed, Digits = 15 is a threshold for described issue. I would like to know, if it is possible to increase the precision of dsolve's solution in order to calculate integrals with higher precision (Digits > 15)?

@Carl Love 

Having tryed all ways above, I see, that the simplest method for calculation of integrals of powers of procedures (u^a) is to write own procedure of numerical integration based on some integration scheme with control of precision and convergence.

@Carl Love 

Here the result of second workaround:

It is a true curse!

@Carl Love 

18.02

@Carl Love 

Dear Carl, integration of u² does not work:

@Axel Vogt 

Thank you, Axel. Es funktioniert.