% HEAT EQUATION BACKWARD-DIFFERENCE ALGORITHM 12.2
%
% To approximate the solution to the parabolic partial-differential
% equation subject to the boundary conditions
% u(0,t) = u(l,t) = 0, 0 < t < T = max t,
% and the initial conditions
% u(x,0) = F(x), 0 <= x <= l:
%
% INPUT: endpoint l; maximum time T; constant ALPHA; integers m, N.
%
% OUTPUT: approximations W(I,J) to u(x(I),t(J)) for each
% I = 1, ..., m-1 and J = 1, ..., N.
syms('OK', 'FX', 'FT', 'ALPHA', 'M', 'N', 'M1', 'M2', 'N1');
syms('H', 'K', 'VV', 'I', 'W', 'L', 'U', 'J', 'T', 'Z');
syms('I1', 'FLAG', 'NAME', 'OUP', 'X', 's', 'x');
TRUE = 1;
FALSE = 0;
fprintf(1,'This is the Backward-Difference Method for Heat
Equation.\n');
fprintf(1,'Input the function F(X) in terms of x.\n');
fprintf(1,'For example: sin(pi*x)\n');
s = input(' ','s');
F = inline(s,'x');
fprintf(1,'The lefthand endpoint on the X-axis is 0.\n');
OK = FALSE;
while OK == FALSE
fprintf(1,'Input the righthand endpoint on the X-axis.\n');
FX = input(' ');
if FX <= 0
fprintf(1,'Must be positive number.\n');
else
OK = TRUE;
end;
end;
OK = FALSE;
while OK == FALSE
fprintf(1,'Input the maximum value of the time variable T.\n');
FT = input(' ');
if FT <= 0
fprintf(1,'Must be positive number.\n');
else
OK = TRUE;
end;
end;
fprintf(1,'Input the constant alpha.\n');
ALPHA = input(' ');
OK = FALSE;
while OK == FALSE
fprintf(1,'Input integer m = number of intervals on X-axis\n');
fprintf(1,'and N = number of time intervals - on separate lines.\n');
fprintf(1,'Note that m must be 3 or larger.\n');
M = input(' ');
N = input(' ');
if M <= 2 | N <= 0
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