@vv 

I thought there would be something simpler and shorter.

Thanks for answer.

I will test it.

Thanks.

frac functon replaced by another functions:

    frac(t) = t-floor(t) = 1/2-I*ln(-exp((2*I)*Pi*t))/(2*Pi) = 1/2-arctan(cot(Pi*t))/Pi

plot([frac(t), t-floor(t), 1/2-I*ln(-exp((2*I)*Pi*t))/(2*Pi), 1/2-arctan(cot(Pi*t))/Pi], t = 0 .. 3.2, legend = [typeset("Curve: ", frac(t)), typeset("Curve: ", t-floor(t)), typeset("Curve: ", 1/2-I*ln(-exp((2*I)*Pi*t))/(2*Pi)), typeset("Curve: ", 1/2-arctan(cot(Pi*t))/Pi)])

For integrals may this helps:

http://12000.org/my_notes/CAS_integration_tests/index.htm

http://12000.org/my_notes/ten_hard_integrals/index.htm

The DirectSearch package will solve your problems, as Mr. Markiyan Hirnyk suggested.

@ernilesh80 

Download summation..mw

@kuwait1 

Well, if alpha =3 in function RootOf you have a equation 5 degree:

sol := {x = b*RootOf(16*_Z^5*b^4-32*V*_Z^4*b^3+24*V^2*_Z^3*b^2-8*V^3*_Z^2*b+V^4*_Z-3*V^3*W*a)/a, y = RootOf(16*_Z^5*b^4-32*V*_Z^4*b^3+24*V^2*_Z^3*b^2-8*V^3*_Z^2*b+V^4*_Z-3*V^3*W*a)}

if alpha =4 in function RootOf you have a equation 6 degree:

sol := {x = b*RootOf(32*_Z^6*b^5-80*V*_Z^5*b^4+80*V^2*_Z^4*b^3-40*V^3*_Z^3*b^2+10*V^4*_Z^2*b-V^5*_Z+4*V^4*W*a)/a, y = RootOf(32*_Z^6*b^5-80*V*_Z^5*b^4+80*V^2*_Z^4*b^3-40*V^3*_Z^3*b^2+10*V^4*_Z^2*b-V^5*_Z+4*V^4*W*a)}

These equations can only be solved in some cases symbolicaly,but in our case this is not possible, can be done only numerically.

An Example see worksheet:

Download Example.mw

For more see:

https://en.wikipedia.org/wiki/Quintic_function

https://en.wikipedia.org/wiki/Sextic_equation

@Leinegold 

Can you clarify the question?

For backup yours work (worksheet) Use : Tools->Option..->General->Auto save-> x minute

:)

@dellair 

It seems a bug in Maple 2016.2 or earlier version.

Using: evalf(Int(evalf(fe11_1), p = 1 .. 9, method = _Dexp)) I'm speed up caluculation for 500 times.

See file attached.

evalfandintPerformance_ver2.mw

@dellair 

Try add first:

Digits := 16;

Checked with Maple 2016.2 on Windows 8.1.

Thank you for a extensive reply.

@tomleslie 

Edited 13.02.2017.

I'm corrrcted my answer.

Better way to solve is numerical,but Mape can't handle nonlinear -elliptic PDE.

I'm use a finite difference schemes,and works.

Here you can find the necessary information that can help you: http://mathematica.stackexchange.com/questions/137494/steady-transonic-gas-flow-nonlinear-pde-giving-initial-condition-and-boundary-va

PDE_-finite_case_2.mw

@Zeineb 

Can you add some background information to the equation?  Maybe yours boundary conditions are wrong?

ALREADY I understood.Thanks

@Markiyan Hirnyk