% RUNGE-KUTTA-FEHLBERG ALGORITHM 5.3
%
% 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 THE MINIMUM STEPSIZE WAS EXCEEDED.
syms('F', 'OK', 'A', 'B', 'ALPHA', 'TOL', 'HMIN', 'HMAX', 'FLAG');
syms('NAME', 'OUP', 'H', 'T', 'W', 'K1', 'K2', 'K3', 'K4', 'K5', 'K6');
syms('R', 'DELTA', 't', 's');
TRUE = 1;
FALSE = 0;
fprintf(1,'This is the Runge-Kutta-Fehlberg Method.\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;
fprintf(1,'Input the initial condition\n');
ALPHA = input(' ');
OK = FALSE;
while OK == FALSE
fprintf(1,'Input tolerance\n');
TOL = input(' ');
if TOL <= 0
fprintf(1,'Tolerance must be a positive.\n');
else
OK = TRUE;
end;
end;
OK = FALSE;
while OK == FALSE
fprintf(1,'Input minimum and maximum mesh spacing on separate
lines.\n');
HMIN = input(' ');
HMAX = input(' ');
if HMIN < HMAX & HMIN > 0
OK = TRUE;
else
fprintf(1,'Minimum mesh spacing must be a positive real\n');
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