# Find the roots of transcendental algebraic equations

조회 수: 2 (최근 30일)
University 2024년 3월 13일
편집: Torsten 2024년 3월 13일
Hello, I have a transcendental equation that has real and imaginary roots. I used MAPLE to solve the algebraic equation but it MAPLE root finder seems to skip some roots. Please can anyone help to solve the problem with MATLAB.
I want the following:
1. Compute the roots of equation q, using the second the equation
2. Use the computed roots to compute $\tau$ using the first equation.Computes the minimum values of real part of tau xi = (-0.3, 0.3) and u=(0,3).
3. Plot contour of the minimum values of real part of tau for xi = (-0.3, 0.3) and u=(0,3) and chi_a = 1.219 × e-6.
alpha3 = -0.001104;
alpha4 = 0.0826;
alpha6 = -0.0336;
gamma1 = 0.1093;
K1 = 6e-12;
d = 200 microns
chi_a = 1.219 × e-6.
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University 2024년 3월 13일
This was the same problem I was facing in MAPLE. I would apprepriate if you can help out.
Torsten 2024년 3월 13일
편집: Torsten 2024년 3월 13일
@Star Strider suggested scanning the function - maybe it will work if you don't know anything about the root(s) you expect to get. For the example given, only q=0 seems to solve the equation:
% Define parameters
alpha3 = -0.001104;
alpha4 = 0.0826;
alpha6 = -0.0336;
gamma1 = 0.1093;
K1 = 6e-12;
d = 200e-6; % microns to meters
chi_a = 1.219e-6;
% Compute Hc
Hc_val = pi / d * sqrt(K1 / chi_a);
% Compute eta1 and alpha
eta1_val = 0.5 * (alpha3 + alpha4 + alpha6);
alpha_val = 1 - alpha3^2 / (gamma1 * eta1_val);
xi = 0.2;
u = 1.5;
q_eqn = @(q) q - (1 - alpha_val) * tan(q) + (alpha3 * xi / eta1_val * tan(q) + chi_a * (u * Hc_val)^2 * q) / gamma1 * (alpha_val * gamma1 * ((4 * K1 * q^2 / d^2) - (alpha3 * xi / eta1_val) - chi_a * (u * Hc_val)^2).^(-1));
q = -80:0.001:80;
fq = arrayfun(@(q)q_eqn(q),q);
qq=q(abs(fq)<1e-10).'
qq = 0

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