% LINEAR FINITE-DIFFERENCE ALGORITHM 11.3
%
% To approximate the solution of the boundary-value problem
%
% Y'' = P(X)Y' + Q(X)Y + R(X), A<=X<=B, Y(A) = ALPHA, Y(B) = BETA:
%
% INPUT: Endpoints A, B; boundary conditions ALPHA, BETA;
% integer N.
%
% OUTPUT: Approximations W(I) to Y(X(I)) for each I=0,1,...,N+1.
syms('OK', 'AA', 'BB', 'ALPHA', 'BETA', 'N', 'FLAG', 'NAME');
syms('OUP', 'H', 'X', 'A', 'B', 'D', 'M', 'I', 'C', 'L', 'U');
syms('Z', 'W', 'J', 's', 'x');
TRUE = 1;
FALSE = 0;
fprintf(1,'This is the Linear Finite-Difference Method.\n');
fprintf(1,'Input the functions P(X), Q(X) and R(X) in terms of x, \n');
fprintf(1,'on separate lines.\n');
fprintf(1,'For example: -2/x \n');
fprintf(1,' 2/(x^2) \n');
fprintf(1,' sin(log(x))/(x^2)\n');
s = input(' ','s');
P = inline(s,'x');
s = input(' ','s');
Q = inline(s,'x');
s = input(' ','s');
R = inline(s,'x');
OK = FALSE;
while OK == FALSE
fprintf(1,'Input left and right endpoints on separate lines.\n');
AA = input(' ');
BB = input(' ');
if AA >= BB
fprintf(1,'Left endpoint must be less than right endpoint.\n');
else
OK = TRUE;
end;
end;
fprintf(1,'Input Y( %.10e).\n', AA);
ALPHA = input(' ');
fprintf(1,'Input Y( %.10e).\n', BB);
BETA = input(' ');
OK = FALSE;
while OK == FALSE
fprintf(1,'Input an integer > 1 for the number of\n');
fprintf(1,'subintervals. Note that h = (b-a)/(n+1)\n');
N = input(' ');
if N <= 1
fprintf(1,'Number must exceed 1.\n');
else
OK = TRUE;
end;
end;
if OK == TRUE
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