@vv 

Oh, Yes my silly mistake.With correction answers are the same. 

Thanks.

@vv 

About volume, Mathematica gave me a different results:

@Ronan 

I2 := 2;

Optimization:-NLPSolve(I2*(I3-I1)/((I3-I2)*(I2-I1)), {I1+I2 >= I3, 0 <= I1, I1 <= I2, I2 <= I3}, assume = nonnegative);

#[Float(infinity), [I1 = 1., I3 = 2.]]

It's seems Maple FAILS in this case I3 = 2 ?

@rlopez 

Thanks for explanation.

Simulation in  MMA and another stuff.

@ecterrab 

It means that pdsolve is design to not solving PDE with weak solution?

Answer is simple, Maple is not a magic box that'll spit out a solution to any problem.

https://www.12000.org/my_notes/pde_in_CAS/pde_in_cas.htm

Probably  tripel integral is equal to Zero. My crystall ball that says.

Where is the integral ?

What have you tried?

@vv 

Workarounds always exist,but disgust always remains.

Thanks.

@Rouben Rostamian  

de := diff(u(x), x, x)+u(x)*(diff(u(x), x))-u(x) = exp(2*x);

bc := u(0) = exp(0), u(1) = exp(1);

dsol := dsolve({bc, de}, numeric,range = -1 .. 2);

plots:-odeplot(dsol, x = -1 .. 2, view = 0 .. 3);

dsol(2);

#Warnings and Errors ?

Where is my plot on rage -1..2 ?

It seems Mathematica is smarter than Maple.

@acer 

Thanks :)

@tschuermann 

Yes,I have this errors messagess from FindRoot.

Increasing in ParametricNDSolve to WorkingPrecision -> 25 helps.

My code is terribly slow and  needs to  completely for rework.

I do not have time for such a job.

I not a guru in Mathematica I'm still learning.

Maybe you can ask here.

HeunC_ver2.zip

@tschuermann 

For  table 40x40  and more probably you  need increase:

1.Digits:                      15 or 20

2.In dsolve:                abserr = 0.1e-50 ?

3. In dsolve:               changing: method=numericmethod (maybe there is a better method(faster))

4. In findroot code:   {guard::posint:=1,maxtries::posint:=1600} ?Explanation for these number See link. For table 40x40 is: posint:=1600

For sure computation times  increase very quickly.