Mariusz Iwaniuk

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These are questions asked by Mariusz Iwaniuk

Hello.

I have a Pde solution in from of the sum.

pde := diff(u(x, t), t) = diff(u(x, t), x$2)

symbolic := pdsolve([pde, u(x, 0) = 1, u(0, t) = 0, u(1, t) = 0])

symbolic := u(x, t) = Sum(-(2*((-1)^_Z9-1))*sin(_Z9*Pi*x)*exp(-Pi^2*_Z9^2*t)/(Pi*_Z9), _Z9 = 1 .. infinity)

 

I tried a subs or eval command dosen't work.

 

Thanks.

pdex1.mw
 

restart

pde := diff(u(x, t), t) = diff(u(x, t), `$`(x, 2)):

ics := [u(x, 0) = 1, u(0, t) = 0, u(1, t) = 0]:

pds := pdsolve(pde, ics, numeric, time = t, range = 0 .. 1, spacestep = 1/4024, timestep = 1/4024):

symbolic := pdsolve([pde, u(x, 0) = 1, u(0, t) = 0, u(1, t) = 0])

u(x, t) = Sum(-2*((-1)^_Z9-1)*sin(_Z9*Pi*x)*exp(-Pi^2*_Z9^2*t)/(Pi*_Z9), _Z9 = 1 .. infinity)

(1)

eval(rhs(symbolic), `~`[_Z9] = n)

Sum(-2*((-1)^_Z9-1)*sin(_Z9*Pi*x)*exp(-Pi^2*_Z9^2*t)/(Pi*_Z9), _Z9 = 1 .. infinity)

(2)

subs(`~`[_Z9] = n, rhs(symbolic))

Sum(-2*((-1)^_Z9-1)*sin(_Z9*Pi*x)*exp(-Pi^2*_Z9^2*t)/(Pi*_Z9), _Z9 = 1 .. infinity)

(3)

subs[eval](`~`[_Z9] = n, rhs(symbolic))

Sum(-2*((-1)^_Z9-1)*sin(_Z9*Pi*x)*exp(-Pi^2*_Z9^2*t)/(Pi*_Z9), _Z9 = 1 .. infinity)

(4)

``


 

Download pdex1.mw

 

Example 6 from Maple Help.

 

restart:

with(Optimization):

LPSolve(2*x+5*y, {3*x-y = 1, x-y <= 5}, assume = {integer, nonnegative})

 

Kernel crash the same with Maple 2015.

 

Does anyone can confirm?

Mariusz Iwaniuk

Hello everybody.

I have a function:

f(x,y)=GAMMA(y, -ln(x))/GAMMA(y)

seq(sum(f(x, y), y = 0 .. 1), x = 0 .. 5)

 

and I got a error message:

Error, (in ln) numeric exception: division by zero ??
This is normal behavior in seq function or Bug?

 

but  when I'm first calculate the sum sol := sum(f(x, y), y = 0 .. 1) -> x,

and evalf([seq(sol, x = 0 .. 5)]) ->[0., 1., 2., 3., 4., 5.] works fine.

 

Seq-division_by_zero.mw

Mariusz Iwaniuk

Hello guys,

I was just playing around with differential equations, when I noticed that symbolic solution is  different from the numerical.What is the reason for this strange behavior?


ODE := (diff(y(x), x))*(ln(y(x))+x) = 1

sol := dsolve({ODE, y(1) = 1}, y(x))

a := plot(op(2, sol), x = .75 .. 2, color = "Red");
sol2 := dsolve([ODE, y(1) = 1], numeric, range = .75 .. 2);

with(plots);
b := odeplot(sol2, .75 .. 2, thickness = 4);
display({a, b});

 

 

Strange_issue.mw

Mariusz Iwaniuk

Hello.

int(floor(x^2), x = 0 .. 2) = 6 , but it should be 1.85374.

 

 

Bug_in_integrate(floor_and_ceil).mw

Mariusz Iwaniuk

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