From 5e792d5e1ac0c1898468aa0d66c629153fd096c4 Mon Sep 17 00:00:00 2001
From: Thomas West <tw00956@surrey.ac.uk>
Date: Tue, 3 Sep 2024 15:24:29 +0000
Subject: [PATCH] Kepler function.
---
Function/Kepler.m | 35 +++++++++++++++++++++++++++++++++++
1 file changed, 35 insertions(+)
create mode 100644 Function/Kepler.m
diff --git a/Function/Kepler.m b/Function/Kepler.m
new file mode 100644
index 0000000..671a84f
--- /dev/null
+++ b/Function/Kepler.m
@@ -0,0 +1,35 @@
+% (W2.1)
+
+function [E, no_of_iterations] = Kepler(e, M, tol)
+
+% Initialize the estimate of E with M
+E = M;
+
+% Set a maximum number of iterations
+max_iterations = 100;
+for ii = 1:max_iterations
+
+ f = M - E + e * sin(E); % evaluate function with respect to E
+ fp = -1 + e * cos(E); % evaluate first derivative with respect E
+
+ % Print output
+ % fprintf('E: %f, |f(E)|: %e\n', E, abs(f));
+
+ % Note: Un-note the above code to see all the convergencies, it is
+ % currently noted as it computes a lot of unnecessary data into the
+ % command window. The script still outputs the correct value of 'E’.
+
+
+ % check for convergence using IF statement
+ if(abs(f) < tol)
+ break;
+ else
+ % Newton's method
+ dE = -f/fp; % delta E
+ E = E + dE; % update estimate of E
+ end
+end
+
+no_of_iterations = ii;
+
+end
\ No newline at end of file
--
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