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Rakshak

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I am trying to solve this coupled PDEs. ...

Rakshak 155 Maple 2018
pde pdsolve differential-equations
September 28 2022
1 3
> 

restart
> 

eq1 := (2*(r^2+a^2*cos(theta)^2))*(M*r-(1/2)*a^2-(1/2)*r^2)*(diff(f(r, theta), r, theta))+(2*(a^2*(M-r)*cos(theta)^2-M*r^2+a^2*r))*(diff(f(r, theta), theta))

2*(r^2+a^2*cos(theta)^2)*(M*r-(1/2)*a^2-(1/2)*r^2)*(diff(diff(f(r, theta), r), theta))+2*(a^2*(M-r)*cos(theta)^2-M*r^2+a^2*r)*(diff(f(r, theta), theta))

 (1)
> 

eq2 := sin(theta)*(r^2+a^2*cos(theta)^2)*(diff(f(r, theta), theta, theta))-cos(theta)*(diff(f(r, theta), theta))*(a^2*cos(theta)^2-2*a^2-r^2)

sin(theta)*(r^2+a^2*cos(theta)^2)*(diff(diff(f(r, theta), theta), theta))-cos(theta)*(diff(f(r, theta), theta))*(a^2*cos(theta)^2-2*a^2-r^2)

 (2)
> 

eq3 := -2*(r^2+a^2*cos(theta)^2)^2*(M*r-(1/2)*a^2-(1/2)*r^2)*sin(theta)*(diff(g(r, theta), r, r))+sin(theta)*(r^2+a^2*cos(theta)^2)^2*(diff(g(r, theta), theta, theta))+(4*(-(1/4)*cos(theta)^4*a^4+a^2*r*(M-(1/2)*r)*cos(theta)^2-M*a^2*r-(1/4)*r^4))*cos(theta)*(diff(g(r, theta), theta))-2*M*sin(theta)*(diff(g(r, theta), r))*(a^2+r^2)*(cos(theta)*a-r)*(cos(theta)*a+r)

-2*(r^2+a^2*cos(theta)^2)^2*(M*r-(1/2)*a^2-(1/2)*r^2)*sin(theta)*(diff(diff(g(r, theta), r), r))+sin(theta)*(r^2+a^2*cos(theta)^2)^2*(diff(diff(g(r, theta), theta), theta))+4*(-(1/4)*cos(theta)^4*a^4+a^2*r*(M-(1/2)*r)*cos(theta)^2-M*a^2*r-(1/4)*r^4)*cos(theta)*(diff(g(r, theta), theta))-2*M*sin(theta)*(diff(g(r, theta), r))*(a^2+r^2)*(cos(theta)*a-r)*(cos(theta)*a+r)

 (3)
> 

pdsolve([eq1, eq2, eq3])

[{f(r, theta) = _F1(r)+(Int((r^2+a^2*cos(theta)^2)/((cos(theta)+1)^(1/2)*(cos(theta)-1)^(1/2)), theta))*_C1/(2*M*r-a^2-r^2)}, [diff(diff(g(r, theta), r), r) = (sin(theta)*(sin(theta)^2*a^2-a^2-r^2)^2*(diff(diff(g(r, theta), theta), theta))-4*cos(theta)*((1/4)*a^4*sin(theta)^4+(-(1/2)*a^2+r*(M-(1/2)*r))*a^2*sin(theta)^2+(1/4)*(a^2+r^2)^2)*(diff(g(r, theta), theta))+2*M*sin(theta)*(diff(g(r, theta), r))*(a^2+r^2)*(sin(theta)^2*a^2-a^2+r^2))/(sin(theta)*(sin(theta)^2*a^2-a^2-r^2)^2*(2*M*r-a^2-r^2))]]

 (4)
> 

``

Download pde1.mw

Is there a way to reduce fontsize while ...

Rakshak 155 Maple
font pdf export
September 07 2022
0 1

Currrently maple exports it in huge fonts do the pdf is really big. I would like to make the pdf smaller by decreaseasing the font size. I cant seem to find any options for that online.

skipping time consuming calculations in ...

Rakshak 155 Maple
loop timelimit
September 03 2022
1 0

I am looping over a list of functions to calculate various properties of the said functions. some of these calculations take too long. I was wondering if there was a way to skip to the next element of the loop if a calculation takes more than a specific time.

What does this error mean in pdsolve?...

Rakshak 155 Maple 2018
pde pdsolve differential-equations
August 31 2022
2 5
> 

eq1 := f(r)*((diff(g(t, phi, r), t))*a^2+(diff(g(t, phi, r), t))*r^2+a*(diff(g(t, phi, r), phi)))/(sqrt(-g(t, phi, r)^2*f(r)^2+1)*sqrt(-(r^2+a^2*cos(theta)^2)*(2*M*r-a^2-r^2)))

f(r)*((diff(g(t, phi, r), t))*a^2+(diff(g(t, phi, r), t))*r^2+a*(diff(g(t, phi, r), phi)))/((-g(t, phi, r)^2*f(r)^2+1)^(1/2)*(-(r^2+a^2*cos(theta)^2)*(2*M*r-a^2-r^2))^(1/2))

 (1)
> 

eq2 := (((-a*cos(theta)^2+a)*f(r)^2*g(t, phi, r)^2+a*cos(theta)^2-a)*(diff(g(t, phi, r), phi, t))+(g(t, phi, r)^2*f(r)^2-1)*(diff(g(t, phi, r), phi, phi))+(-(diff(g(t, phi, r), phi))+(diff(g(t, phi, r), t))*a*(cos(theta)-1)*(cos(theta)+1))*(diff(g(t, phi, r), phi))*f(r)^2*g(t, phi, r))*f(r)/((-g(t, phi, r)^2*f(r)^2+1)^(3/2)*sin(theta))

(((-a*cos(theta)^2+a)*f(r)^2*g(t, phi, r)^2+a*cos(theta)^2-a)*(diff(diff(g(t, phi, r), phi), t))+(g(t, phi, r)^2*f(r)^2-1)*(diff(diff(g(t, phi, r), phi), phi))+(-(diff(g(t, phi, r), phi))+(diff(g(t, phi, r), t))*a*(cos(theta)-1)*(cos(theta)+1))*(diff(g(t, phi, r), phi))*f(r)^2*g(t, phi, r))*f(r)/((-g(t, phi, r)^2*f(r)^2+1)^(3/2)*sin(theta))

 (2)
> 

pdsolve([eq1, eq2])

Error, (in pdsolve/sys) found the element '_F4' repeated in the indication of blocks variables

  
> 

``

Download problemfile.mw

I am trying to solve these two coupled PDE and am getting this error. Does anyone know what this mean?

permute into a list of sums...

Rakshak 155 Maple
combinatorics permutation
August 27 2022
1 0

I was wondering if there was a way to permute a list to get a list of sums of permutations.
for example,

list:=[a,b,c]
permute(list,2) gives me ([a,b] [b,c] [c,a])

I would like to get this instead: ([a+b],[b+c],[c+d])

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