Added Functions and Scripts

1 files changed, 44 insertions, 0 deletions

diff --git a/Functions/Heun/Heun.m b/Functions/Heun/Heun.m
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+++ b/Functions/Heun/Heun.m
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+function [t,y] = Heun(dydt,tspan,y0,h,es,maxit)
+% [t,y] = Heun(dydt,tspan,y0,h): uses the heun method to integrate an ODE
+% inputs:
+%	dydt = the differential equation of interest (must be anonymous
+%		function)
+%	tspan = [ti,tf] the initial and final values of the independent
+%		variable
+%	y0 = the initial value of the dependent variable
+%	h = step size
+%	es = stopping criterion (%), optional (default = 0.001)
+%	maxit = maximum iterations of corrector, optional (default = 50)
+% outputs:
+%	t = vector of independent variable values
+%	y = vector of solution for dependent variable  
+
+%Error checking
+if nargin<4, error('At least 4 aruments required.');end
+if nargin<5|isempty(es), es = 0.001;end
+if nargin<6|isempty(maxit), maxit = 50;end
+if length(tspan)~=2, error('Argument tspan must have a length of 2');end 
+
+%Trims tspan according to step size (h)
+t=tspan(1):h:tspan(2);
+%if rem(tspan(2),h)~=0
+if t(length(t))~=tspan(2)
+    t=[t,tspan(end)];
+end
+
+y=ones(1,length(t))*y0;
+h=diff(t);
+
+for i=1:length(t)-1
+	S=dydt(t(i),y(i));
+	ynew=y(i)+S*h;
+	for j=1:maxit
+		yold=ynew;
+		ynew=y(i)+h(i)/2*(S+dydt(t(i+1),yold));
+		ea = abs((ynew-yold)/ynew)*100;
+		if ea <= es, break, end
+	end
+	y(i+1)=ynew;
+end
+plot(t,y)
+end
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