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Question: Positive root of an equation

Question:Positive root of an equation

sunit 105 Maple
rootfinding
October 10 2013
0

Hi,

I need help for the following,

> 

restart
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with(RootFinding):
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temp := 1.570796327*Omega/arctan(-4.*Omega*(0.1e-1*Omega^4+.596454825*Omega^2+1.085036213)*(Omega^4-5.001916537*Omega^2+6.257294927)*(-1.+Omega^2)/(Omega^12-12.00343307*Omega^10+39.15373981+58.58914143*Omega^8-146.1584484*Omega^6+207.0587674*Omega^4-136.1951992*Omega^2), -(1.*(Omega^12-12.00423307*Omega^10+39.15373981+58.49370865*Omega^8-149.1781211*Omega^6+196.7039658*Omega^4-145.6136279*Omega^2))/(Omega^12-12.00343307*Omega^10+39.15373981+58.58914143*Omega^8-146.1584484*Omega^6+207.0587674*Omega^4-136.1951992*Omega^2))-x:
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#I have to find only positive roots of above equation for different values of x, so i am using followin;
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solve({Omega > 0, subs(x = 1.1, temp)}, Omega)

{Omega = .7794998975}

 (1)
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#But for values greater than 2.1 this is not working, and even for greater than 2.1 positive root exists
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solve(subs(x = 2.2, temp), Omega)

-.8571903591, .8571903591

 (2)
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#The problem with the above procedure is that it is taking time in order to calculate other root, which is not of my use. So my question is, how would i calculate only positive root of temp for different values of x, so that my computation time can be reduced.

I really need help for this.

Regards

Sunit

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