Secant method numerical analysis

How Find all intersections of a function using secant method? What is the code

Answer 1

[Sam Chak]

Hi @Andrew242

This is just a sample code using the Secant Method to find the root of the Kepler’s equation:

function Demo_Secant

close all

clc

% Solving Kepler’s equation: E – e*sin(E) = M

f = @(x) x - 0.37255*sin(x) - 0.8828;

[x, iter] = SecaMeth(f, -pi, pi)

end

function [root, n] = SecaMeth(f, x1, x2, epsilon, N)

% f(x1) and f(x2) are initial points for drawing the secant line connecting them

% epsilon is the tolerance of convergence (default 1e-6),

% N is the maximum number of iterations (default 30),

if nargin < 5 || isempty(N), N = 30; end

if nargin < 4 || isempty(epsilon), epsilon = 1e-6; end

x = zeros(1, N+1);

for n = 2:N

if x1 == x2

root = 'failure';

return

end

x(1) = x1;

x(2) = x2;

x(n+1) = x(n) - ( ( x(n) - x(n-1) )/( f(x(n)) - f(x(n-1)) ) )*f(x(n));

if abs(x(n+1) - x(n)) < epsilon

root = x(n+1);

return

end

end

end

Result:

x =

1.2345

iter =

7

Hope this is helpful for you to modify the code that suits your needs.