Transcendental equation solution by numerical method

Question

Rizwan 2013-11-18

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/106612-transcendental-equation-solution-by-numerical-method

回答： Matt J 2013-11-18

Hello,

I want to solve one transcendental equation numerically. I have used the function 'solve' for the solution but my results are varied as compared to graphical solution. My code is written below and I am sending the graphical solution results.

clear all;
n1=1.77;
n2=1.45;
d=1e-6;
lambda = 1e-6;
ko = 2*pi/lambda;
A=(ko*n1)^2;
B=(ko*n2)^2;
r=(ko*d)*sqrt(n1^2-n2^2);
syms h;
s=((h*d)-m*pi) == 2*atan(sqrt(r^2/(h^2*d^2)-1));
solve (s)
prop=sqrt(A-ans^2);
neff=(prop*lambda)/(2*3.14)

where m will be varries from 0 to 2.0 with interval of 0.5. Graphical results are: m=0 neff is 1.7299 but graphical solution is 1.75 m=0.5 neff is 1.678 but graphical solution is 1.71 m=1.0 neff is 1.608 but graphical solution is 1.65 m=1.5 neff is 1.523 but graphical solution is 1.55 m=2.0 neff is 1.451 but graphical solution is 1.452

Can anyone please help me out and tell me the fault ? Also is there any other function can be used instead of 'solve'.

Thanks.