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RK1

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These are questions asked by RK1

Could anyone help me rewrite the solutio...

RK1 160 Maple
pdsolve
December 04 2022
1 0

pdsol.mw

I am trying to solve a set of simultane...

RK1 160 Maple
integral pde pdsolve
October 14 2022
1 1


 

> 

``
> 

eq1 := -6*sin(theta)*(cos(theta)^2*(diff(n(r, theta), r))*a^3+cos(theta)^2*a^4+3*cos(theta)^2*a^2*r^2+(diff(n(r, theta), r))*a*r^2+2*r^4-n(r, theta)*a*r)/(r^2+cos(theta)^2*a^2)^(3/2) = 0

-6*sin(theta)*(cos(theta)^2*(diff(n(r, theta), r))*a^3+cos(theta)^2*a^4+3*cos(theta)^2*a^2*r^2+(diff(n(r, theta), r))*a*r^2+2*r^4-n(r, theta)*a*r)/(r^2+cos(theta)^2*a^2)^(3/2) = 0

 (1)
> 

eq2 := -(6*(cos(theta)^2*sin(theta)*(diff(n(r, theta), theta))*a^3+a^4*r*cos(theta)+2*cos(theta)*a^2*r^3+cos(theta)*r^5+n(r, theta)*a^3*cos(theta)+cos(theta)*n(r, theta)*a*r^2+sin(theta)*(diff(n(r, theta), theta))*a*r^2))/(r^2+cos(theta)^2*a^2)^(3/2) = 0

-6*(cos(theta)^2*sin(theta)*(diff(n(r, theta), theta))*a^3+a^4*r*cos(theta)+2*cos(theta)*a^2*r^3+cos(theta)*r^5+n(r, theta)*a^3*cos(theta)+cos(theta)*n(r, theta)*a*r^2+sin(theta)*(diff(n(r, theta), theta))*a*r^2)/(r^2+cos(theta)^2*a^2)^(3/2) = 0

 (2)
> 

pdsolve([eq1, eq2])

{n(r, theta) = (1/2)*(4*r^2+2*a^2*cos(2*theta)+2*a^2)^(1/2)*((Int(-2*((a^4+3*a^2*r^2)*cos(2*theta)+a^4+3*r^2*a^2+4*r^4)/((4*r^2+2*a^2*cos(2*theta)+2*a^2)^(1/2)*(a^2*cos(2*theta)+a^2+2*r^2)*a), r))*sin(theta)+Int(5*(a^2*(-(1/5)*(a^2+4*r^2)^2*cos(3*theta)+(-(3/5)*a^4-(8/5)*r^2*a^2)*cos(5*theta)-(1/5)*a^4*cos(7*theta)+cos(theta)*(a^4+(16/5)*r^2*a^2+(16/5)*r^4))*(4*r^2+2*a^2*cos(2*theta)+2*a^2)^(1/2)*(Int(16*((a^2+3*r^2)*cos(2*theta)+a^2-r^2)/(4*r^2+2*a^2*cos(2*theta)+2*a^2)^(5/2), r))-(16/5)*(a^2+r^2)*((-(1/2)*a^2-2*r^2)*cos(3*theta)-(1/2)*a^2*cos(5*theta)+cos(theta)*(a^2+2*r^2))*r)*a/((4*r^2+2*a^2*cos(2*theta)+2*a^2)^(1/2)*((32*a^4+64*a^2*r^2)*cos(2*theta)+8*a^4*cos(4*theta)+24*a^4+64*r^2*a^2+64*r^4)), theta)+_C1)/sin(theta)}, {n(r, theta) = -(a^2*r+r^3)/a}

 (3)
> 

``


 

Download PDE_integral.mw

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

RK1 160 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 ...

RK1 160 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 ...

RK1 160 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.

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