% EULER'S ALGORITHM 5.1
%
% TO APPROXIMATE THE SOLUTION OF THE INITIAL VALUE PROBLEM:
% Y' = F(T,Y), A<=T<=B, Y(A) = ALPHA,
% AT N+1 EQUALLY SPACED POINTS IN THE INTERVAL [A,B].
%
% INPUT: ENDPOINTS A,B; INITIAL CONDITION ALPHA; INTEGER N.
%
% OUTPUT: APPROXIMATION W TO Y AT THE (N+1) VALUES OF T.
syms('F','OK','A','B','ALPHA','N','FLAG','NAME','OUP','H');
syms('T','W','I','x','s');
TRUE = 1;
FALSE = 0;
fprintf(1,'This is Eulers 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 a positive integer for the number of subintervals\n');
N = input(' ');
if N <= 0
fprintf(1,'Number must be a positive integer\n');
else
OK = TRUE;
end;
end;
if OK == TRUE
fprintf(1,'Choice of output method:\n');
fprintf(1,'1. Output to screen\n');
fprintf(1,'2. Output to text file\n');
fprintf(1,'Please enter 1 or 2\n');
FLAG = input(' ');
if FLAG == 2
fprintf(1,'Input the file name in the form - drive:\\name.ext\n');
fprintf(1,'For example A:\\OUTPUT.DTA\n');
NAME = input(' ','s');
OUP = fopen(NAME,'wt');
else
OUP = 1;
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