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.
