Find all possible roots of transcendental function

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University
University 2023-9-8
评论： Sam Chak 2023-9-9
Please can help with how find all the possible roots of q for xi and u and use the results to compute tau?
clear
clc
close all
%% Model parameters
alpha3 = -0.001104; eta1 = 0.0240; K1 = 6*10^(-12);
gamma1 = 0.1093; chi_a = 1.219*10^(-6); d = 0.0002;
H_c = pi*sqrt(K1/chi_a)/d;
alpha = 1-((alpha3).^2/(gamma1*eta1));
xi =linspace(-0.3, 0.3, 81);
u = linspace(0, 3, 81);
for iu=1:length(u)
for ixi=1:length(xi)
q(iu, ixi) - (1-alpha)*tan(q) + (1/gamma1)*((alpha3*ixi/eta1)*tan(q) + chi_a*(iu*H_c)^2*q)*(alpha*gamma1* (4*K1*q(iu, ixi).^2/d.^2 - (alpha3*ixi)/eta1 - chi_a*(iu*H_c).^2)^(-1));
tau(iu, ixi) = (alpha*gamma1*(4*K1*q(iu, ixi).^2/d.^2 - (alpha3*ixi)/eta1 - chi_a*(iu*H_c).^2)^(-1)
end
end
  1 个评论
James Tursa
James Tursa 2023-9-8
Please post an image of the function you are trying to find the roots of, rather than have us trying to decipher your code.

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回答（1 个）

Torsten
Torsten 2023-9-8
编辑：Torsten 2023-9-8
Ran in:
Really all zeros ? Then you cannot save them in any array since for each u and xi, you get an infinite number of them. Is the function correct ? There were some strange settings therein: the "q(iu, ixi) -" at the beginning and the use of ixi and iu instead of xi(ixi) and u(iu) in the function definition.
%% Model parameters
alpha3 = -0.001104; eta1 = 0.0240; K1 = 6*10^(-12);
gamma1 = 0.1093; chi_a = 1.219*10^(-6); d = 0.0002;
H_c = pi*sqrt(K1/chi_a)/d;
alpha = 1-((alpha3).^2/(gamma1*eta1));
fun = @(q,xi,u)(1-alpha).*tan(q) + (1./gamma1).*((alpha3.*xi./eta1).*tan(q) + chi_a.*(u*H_c).^2.*q).*(alpha.*gamma1.*(4.*K1.*q.^2/d.^2-(alpha3.*xi)./eta1-chi_a.*(u.*H_c).^2).^(-1));
xi = 0.2;
u = 1.5;
hold on
q = 0:0.01:pi/2-0.1;
plot(q,fun(q,xi,u),'b')
q = pi/2+0.1:0.01:3*pi/2-0.1;
plot(q,fun(q,xi,u),'b')
q = 3*pi/2+0.1:0.01:5*pi/2-0.1;
plot(q,fun(q,xi,u),'b')
q = 5*pi/2+0.1:0.01:7*pi/2-0.1;
plot(q,fun(q,xi,u),'b')
hold off
grid on
  4 个评论
显示 2更早的评论
University
University 2023-9-9
Thank you Sam. The maple code is a bit long. Unless, you want the complete code. I have attached the contour plot of tau with respect to xi and u
Sam Chak
Sam Chak 2023-9-9
@University, Based on the contour plot, it is most likely that the circled region represents the zero-crossing region where the roots are located. Therefore, the solution should appear as a curved line. However, if we examine the presumed implicit function , which has yet to be clarified, it is possible that this region corresponds to where discontinuities occur due to the tangent function in .

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