general approximation techniques developed from exercise sheets

1 files changed, 25 insertions, 0 deletions

diff --git a/general/euler.m b/general/euler.m
new file mode 100644
index 0000000..72360b8
--- /dev/null
+++ b/general/euler.m
@@ -0,0 +1,25 @@
+function [xa, ya] = euler(derivative, x_initial, y_initial, step, x_final)
+	% Define intial values for x and y
+	%x_initial=0; 
+	%y_initial=2;
+
+	%% Set the step size between calculations
+	%step=0.0003;
+
+	%% Define an endpoint
+	%x_final=1;
+
+	%% Define a dy/dx
+	%derivative=@(x,y) x+y; 
+
+	% Determine how many times to step forward
+	N=round((x_final-x_initial)/step); % use this determine size
+
+	% Define and initialise arrays to contain coordinates
+	ya=zeros(1,N); xa=zeros(1,N);
+	xa(1)=x_initial; ya(1)=y_initial;
+	
+	for j=1:N-1 % loop for N-1 steps
+		ya(j+1)=ya(j) + step*feval(derivative, xa(j),ya(j)); % next value
+		xa(j+1)=xa(j)+step; % increase x by stepsize
+	end