% WAVE EQUATION FINITE-DIFFERENCE ALGORITHM 12.4
%
% To approximate the solution to the wave 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) and Du(x,0)/Dt = G(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 = 0, ..., m
% and J=0,...,N.
syms('OK', 'FX', 'FT', 'ALPHA', 'M', 'N', 'M1', 'M2', 'N1', 'N2');
syms('H', 'K', 'V', 'J', 'W', 'I', 'FLAG', 'NAME', 'OUP', 'X', 's',
'x');
TRUE = 1;
FALSE = 0;
fprintf(1,'This is the Finite-Difference Method for the Wave
Equation.\n');
fprintf(1,'Input the functions F(X) and G(X) in terms of x, \n');
fprintf(1,'on separate lines. \n');
fprintf(1,'For example: sin(pi*x)\n');
fprintf(1,' 0 \n');
s = input(' ','s');
F = inline(s,'x');
s = input(' ','s');
G = 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 a 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 a 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');
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