% AdBash2Driver.m

% This is a driver that inputs the appropriate 
% initial conditions and step size for using the
% function AdBash2.m to solve the IVP given by
%   y' = f(t,y)   y(t0)=y0
% using a Two-Step Adams-Bashforth Method.
% Note that this driver inputs the function f.m
% to obtain function values for f(t,y)
% Note that it uses an Modified-Euler startup.

% Clear Workspace
clear

% Set initial conditions
t0     = Edit;
y0     = Edit;
name   ='UserMustEDITThis'   %string containing
                             %the name of the function
                             %to be evaluated.

% Set step size and number of steps taken in the
% multistep algorithm
h     = Edit;
M     = Edit;


%------------ One-step Startup Here -----------%
% Apply Modified-Euler.m for 1 startup step
[t,y]=ModEul(name,h,1,t0,y0);
%-----------------------------------------------%

%-------- Two-step Adams-Bashforth Here --------%
% Apply AdBash2.m function
[t_vec,y_vec]=AdBash2(name,h,M,t,y)
%-----------------------------------------------%

% t_vec is the vector of t-values from the step
% size given by h.
% y_vec is the corresponding approximations for the
% solution to the IVP.  We can plot the linear interpolant 
% of the approx. solution values along with the true solution 
% to compare.

%-------- Construct True Solution Values --------%
t2 = [t0:0.1*h:t0+(M+1)*h];
%TrueSoln_vec = You put stuff here;
%------------------------------------------------%

%-------------------- Plots ---------------------%
figure(1)
plot(t_vec,y_vec,'g--',t2,TrueSoln_vec,'r-',t_vec,y_vec,'g*');
legend('Two-Step Adams-Bashforth','True Solution');
xlabel('t');
ylabel('y(t)');
%------------------------------------------------%