%  F1_10.m
%  Carol Lucas
%  To make life easy for entering changes, suggest that you set up a
%  matrix in the command window, e.g., set parameters at starting values
%  then move them to a matrix, e.g. to start with text example.
%        tau=3;noinf=.5;noinit=1;h=.2;time=15;
%        A=[tau noinf noinit h time];
%  then just enter A at the prompt signal.  Anytime you change a parameter,
%  just be sure to reactivate the 'A=[...' line.
%  Hitting return without 5 entries leads to default values of F1_10.

clear t no nexact
P=input('Please enter[tau ninf noinitial h time] as row matrix: ');

if length(P)~=5;
	tau=3;noinf=.5;noin=1;h=.2;tend=15;
	else
	tau=P(1);noinf=P(2);noin=P(3);h=P(4);tend=P(5);	
	end;
	
tstart=0;n=1;no(1)=noin;t(1)=tstart;nexact(1)=noin;
figure(1);clf;

plot([tstart tend],[noinf noinf]);
xlabel('time');ylabel('no');
title('dno/dt = -(no-ninf)/tau, euler=blue, exact=green, matlab=red');

axis([tstart tend 0 1]);

hold on;

%  This demonstrates the simplest ode solver - euler, whole step, no correction.


	while t(n)<=tend;

		ndot=(noinf-no(n))/tau;    %  This is usually a function call, e.g.'nofun'
		no(n+1)=no(n)+h*ndot;
		t(n+1)=t(n)+h;
		n=n+1;
		nexact(n)=noinf+(noin-noinf)*exp(-t(n)/tau);
		plot(t(n-1:n),no(n-1:n),'b',t(n-1:n),nexact(n-1:n),'g');pause(.8);

	end

%  CHECK WITH MATLABS ROUTINES

input('Hit any key to see MATLAB ODE SOLVER ode23')


[t1,n1]=ode23('nofun',t,noin,[],tau,noinf);
figure(1);plot(t1,n1,'r');