% RUNGE-KUTTA FOR SYSTEMS OF DIFFERENTIAL EQUATIONS ALGORITHM 5.7
%
% TO APPROXIMATE THE SOLUTION OF THE MTH-ORDER SYSTEM OF FIRST-
% ORDER INITIAL-VALUE PROBLEMS
% UJ' = FJ( T, U1, U2, ..., UM ), J = 1, 2, ..., M
% A <= T <= B, UJ(A) = ALPHAJ, J = 1, 2, ..., M
% AT (N+1) EQUALLY SPACED NUMBERS IN THE INTERVAL (A,B).
%
% INPUT: ENDPOINTS A,B; NUMBER OF EQUATIONS M; INITIAL
% CONDITIONS ALPHA1, ..., ALPHAM; INTEGER N.
%
% OUTPUT: APPROXIMATION WJ TO UJ(T) AT THE (N+1) VALUES OF T.
syms('OK', 'M', 'I', 'A', 'B', 'ALPHA', 'N', 'FLAG');
syms('NAME', 'OUP', 'H', 'T', 'J', 'W', 'L', 'K','s');
syms('K1','K2','K3','K4','Z');
TRUE = 1;
FALSE = 0;
fprintf(1,'This is the Runge-Kutta Method for Systems of m
equations\n');
fprintf(1,'This program uses the file F.m. If the number of
equations\n');
fprintf(1,'exceeds 7, then F.m must be changed.\n');
OK = FALSE;
while OK == FALSE
fprintf(1,'Input the number of equations\n');
M = input(' ');
if M <= 0
fprintf(1,'Number must be a positive integer\n');
else
OK = TRUE;
end;
end;
for I = 1:M
fprintf(1,'Input the function F_(%d) in terms of t and y1 ... y%d\n',
I,M);
fprintf(1,'For example: y1-t^2+1 \n');
s(I) = input(' ','s');
end;
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;
ALPHA = zeros(1,M);
for I = 1:M
fprintf(1,'Input the initial condition alpha(%d)\n', I);
ALPHA(I) = input(' ');
end;
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