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Question: Numerical solution of intersection of two curves over an interval containing asymptotes

Question:Numerical solution of intersection of two curves over an interval containing asymptotes

Vesnog 90 Maple 15
fsolve interval asympt intersection
November 02 2014
0

Hello I am a Maple 15 user and I am using the command fsolve to solve for the intersection of two curves over a specified interval in x, namely from 0 to the lim defined in the Maple document. The specified interval contains asymptotes and when I specify the full interval only one of the three solutions is returned even if I can see that there are three distinct solutions by looking at the plot of RHS and LHS. Should I use another technique to find the solution or is my implementation of fsolve command wrong?

Thanks in advance


restart

with(ListTools):

n1 := 1:

n2 := 1.50:

n3 := 1.40:

lambda := 1.3:

k0 := 2*Pi/lambda:

d := 3:

x0 := k0*d:

arg1 := sqrt(x0^2*(n2^2-n1^2)):

arg2 := sqrt(x0^2*(n2^2-n3^2)):

lim := FindMinimalElement([arg1, arg2]):

sqr1 := sqrt(x0^2*(n2^2-n1^2)-x^2):

sqr2 := sqrt(x0^2*(n2^2-n3^2)-x^2):

LHS := tan(x):

RHS := (sqr1+sqr2)/(x*(1-sqr1*sqr2/x^2)):

plot([LHS, RHS], x = 0 .. lim, y = -6 .. 6)

  

fsolve(RHS = LHS, x = (1/2)*Pi .. 3*Pi*(1/2))

2.634254816

 (1)

fsolve(RHS = LHS, x = 3*Pi*(1/2) .. 9*Pi*(1/4))

5.222527128

 (2)

fsolve(RHS = LHS, x = 9*Pi*(1/4) .. lim)

7.598486053

 (3)

``


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