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Naba zahran

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How to reduce the time for solving compl...

Naba zahran 10
November 23 2014
1 33

I'm working on my master thesis and trying to solve this equation on maple, after I developed my equation and solving it for N=2,3 and then trying to solve it for N=4 and 5 it took so much long time(more than two days without get any answer), so i'm asking you now to help me reducing the time for solving this complicated equation. 

Shklovskii_N_spheres_with_tails.mw

> 

a := .4; lB := .714; R := 3.2; Z := 24; L := 88; `ℓ` := 2*Z/eta; eta := 1; b := .7; N := 4; Lx = (-N*l+L)/N; r = Lx+2*R

.4

  

.714

  

3.2

  

24

  

88

  

48

  

1

  

.7

  

3

  

Lx = 88/3-l

  

r = Lx+6.4

 (1)
> 

F := N*(l*ln(R/a)-l*ln(l/R)+(l-`ℓ`)^2/(2*R))+((N-1)*((L-l)/(N-1)))*ln((L-l)/((N-1)*a))+2*(L-l)*ln((L-l)/((N-1)*a))/(N-1)+sum(((N-q)*(l-`ℓ`)*(l-`ℓ`))/(q*(2*R+l)+(q-1)*(L-l)/(N-1)), q = 1 .. N)+sum((2*N-2*q)*(l-`ℓ`)*ln(((L-l)/(N-1)+(2*q-1)*R+(q-1)*(L-l)/(N-1))/((2*q-1)*R+(q-1)*(L-l)/(N-1))), q = 1 .. N-1)+sum((2*(l-`ℓ`))*ln(((L-l)/(N-1)+(2*q-1)*R+(q-1)*(L-l)/(N-1))/((2*q-1)*R+(q-1)*(L-l)/(N-1))), q = 1 .. N)+sum((N-q-1)*((2*(L-l)/(N-1)+2*q*R+(q-1)*(L-l)/(N-1))*ln(2*(L-l)/(N-1)+2*q*R+(q-1)*(L-l)/(N-1))-2*((L-l)/(N-1)-2*q*R+(q-1)*(L-l)/(N-1))*ln((L-l)/(N-1)-2*q*R+(q-1)*(L-l)/(N-1))+(2*q*R+(q-1)*(L-l)/(N-1))*ln(2*q*R+(q-1)*(L-l)/(N-1))), q = 1 .. N-1)+sum(2*((2*(L-l)/(N-1)+2*q*R+(q-1)*(L-l)/(N-1))*ln(2*(L-l)/(N-1)+2*q*R+(q-1)*(L-l)/(N-1))-2*((L-l)/(N-1)-2*q*R+(q-1)*(L-l)/(N-1))*ln((L-l)/(N-1)-2*q*R+(q-1)*(L-l)/(N-1))+(2*q*R+(q-1)*(L-l)/(N-1))*ln(2*q*R+(q-1)*(L-l)/(N-1))), q = 1 .. N-1)+(2*(L-l)/(N-1)+2*N*R+(N-1)*((L-l)/(N-1)))*ln(2*(L-l)/(N-1)+2*N*R+(N-1)*((L-l)/(N-1)))-2*((L-l)/(N-1)+2*N*R+(N-1)*((L-l)/(N-1)))*ln((L-l)/(N-1)+2*N*R+(N-1)*((L-l)/(N-1)))+(2*N*R+(N-1)*((L-l)/(N-1)))*ln(2*N*R+(N-1)*((L-l)/(N-1)))

6.238324626*l-3*l*ln(.3125000000*l)+.4687500000*(l-48)^2+2*(88-l)*ln(110.0000000-1.250000000*l)+2.*(l-48.)^2/(6.400000000+l)+(l-48.)^2/(56.80000000+1.500000000*l)+6.*(l-48.)*ln(14.75000000-.1562500000*l)+4.*(l-48.)*ln((97.60000000-1.*l)/(53.60000000-.5000000000*l))+2.*(l-48.)*ln((148.-1.500000000*l)/(104.-1.*l))+3.*(94.40000000-1.*l)*ln(94.40000000-1.*l)-6.*(37.60000000-.5000000000*l)*ln(37.60000000-.5000000000*l)+35.64092141+2.*(144.8000000-1.500000000*l)*ln(144.8000000-1.500000000*l)-4.*(75.20000000-1.*l)*ln(75.20000000-1.*l)+2.*(56.80000000-.5000000000*l)*ln(56.80000000-.5000000000*l)+(195.2-2*l)*ln(195.2-2*l)-2*(151.2-(3/2)*l)*ln(151.2-(3/2)*l)+(107.2-l)*ln(107.2-l)

 (2)
> 

s := diff(F, l)

.9375000000*l-3*ln(.3125000000*l)+4.*(l-48.)/(6.400000000+l)-2.*(l-48.)^2/(6.400000000+l)^2-41.76167537-2*ln(110.0000000-1.250000000*l)-2.500000000*(88-l)/(110.0000000-1.250000000*l)-1.500000000*(l-48.)^2/(56.80000000+1.500000000*l)^2-.9375000000*(l-48.)/(14.75000000-.1562500000*l)-3.000000000*ln(144.8000000-1.500000000*l)+4.*ln(75.20000000-1.*l)-1.000000000*ln(56.80000000-.5000000000*l)+2*(l-48.)/(56.80000000+1.500000000*l)+2.*(l-48.)*(-1.500000000/(104.-1.*l)+1.*(148.-1.500000000*l)/(104.-1.*l)^2)*(104.-1.*l)/(148.-1.500000000*l)+6.*ln(14.75000000-.1562500000*l)+4.*ln((97.60000000-1.*l)/(53.60000000-.5000000000*l))+2.*ln((148.-1.500000000*l)/(104.-1.*l))+4.*(l-48.)*(-1./(53.60000000-.5000000000*l)+.5000000000*(97.60000000-1.*l)/(53.60000000-.5000000000*l)^2)*(53.60000000-.5000000000*l)/(97.60000000-1.*l)-3.*ln(94.40000000-1.*l)+3.000000000*ln(37.60000000-.5000000000*l)-2*ln(195.2-2*l)+3*ln(151.2-(3/2)*l)-ln(107.2-l)

 (3)
> 

solve(s, l)

104.4945628

 (4)
> 

NULL



Download Shklovskii_N_spheres_with_tails.mwShklovskii_N_spheres_with_tails.mw

 

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