% EXTRAPOLATION ALGORITHM 5.6
%
% To approximate the solution of the initial value problem:
% y' = f(t,y), a <= t <= b, y(a) = ALPHA,
% with local truncation error within a given tolerance:
%
% INPUT: endpoints a,b; initial condition ALPHA; tolerance TOL;
% maximum stepsize HMAX; minimum stepsize HMIN.
%
% OUTPUT: T, W, H where W approximates y(T) and stepsize H was
% used or a message that minimum stepsize was exceeded.
syms('F', 'OK', 'A', 'B', 'ALPHA', 'TOL', 'HMIN', 'HMAX');
syms('FLAG', 'NAME', 'OUP', 'NK', 'J', 'I', 'T0', 'W0');
syms('H', 'DONE', 'Q', 'K', 'NFLAG', 'HK', 'T', 'W2');
syms('W3', 'M', 'W1', 'Y', 'V','t','y');
TRUE = 1;
FALSE = 0;
fprintf(1,'This is Gragg Extrapolation\n');
fprintf(1,'Input the function F(t,y) in terms of t and y\n');
fprintf(1,'For example: y-t^2+1 \n');
s = input(' ','s');
F = inline(s,'t','y');
OK = FALSE;
while OK == FALSE
fprintf(1,'Input left and right endpoints on separate lines.\n');
A = input(' ');
B = input(' ');
if A >= B
fprintf(1,'Left endpoint must be less than right endpoint.\n');
else
OK = TRUE;
end;
end;
OK = FALSE;
fprintf(1,'Input the initial condition.\n');
ALPHA = input(' ');
while OK == FALSE
fprintf(1,'Input tolerance.\n');
TOL = input(' ');
if TOL <= 0
fprintf(1,'Tolerance must be positive.\n');
else
OK = TRUE;
end;
end;
OK = FALSE;
while OK == FALSE
fprintf(1,'Input minimum and maximum mesh spacing ');
fprintf(1,'on separate lines.\n');
HMIN = input(' ');
HMAX = input(' ');
if HMIN < HMAX & HMIN > 0
OK = TRUE;
else
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