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function [xa, ya] = midpoint(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;
	
	% da is the value of the derivative at xa, ya
	for j=1:N-1 % loop for N-1 steps
		da = feval(derivative, xa(j), ya(j));
		ya(j+1)=ya(j) + step*feval(derivative, xa(j)+step/2, ya(j)+step/2*da); 
		xa(j+1)=xa(j)+step; % increase x by stepsize
	end