% RUNGE-KUTTA (ORDER 4) ALGORITHM 5.2
 %
 % TO APPROXIMATE THE SOLUTION TO THE INITIAL VALUE PROBLEM:
 %            Y' = F(T,Y), A<=T<=B, Y(A) = ALPHA,
 % AT (N+1) EQUALLY SPACED NUMBERS 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');
 syms('H', 'T', 'W', 'I', 'K1', 'K2', 'K3', 'K4','t','d');
 TRUE = 1;
 FALSE = 0;
 fprintf(1,'This is the Runge-Kutta Order Four 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;
 end;
 fprintf(OUP, 'RUNGE-KUTTA FOURTH ORDER METHOD\n\n');
 fprintf(OUP, '    t           w\n\n');
% STEP 1
 H = (B-A)/N;
 T = A;
 W = ALPHA;
 fprintf(OUP, '%5.3f %11.7f\n', T, W);
% STEP 2
 for I = 1:N 
% STEP 3
% use K1, K2, K3, K4 for K(1), K(2), K(3), K(4) RESP.
 K1 = H*F(T,W);
 K2 = H*F(T+H/2.0, W+K1/2.0);
 K3 = H*F(T+H/2.0, W+K2/2.0);
 K4 = H*F(T+H,W+K3);
% STEP 4
% compute W(I)
 W = W+(K1+2.0*(K2+K3)+K4)/6.0;
% compute T(I)
 T = A+I*H;
% STEP 5
 fprintf(OUP, '%5.3f %11.7f\n', T, W);
 end;
% STEP 6
 if OUP ~= 1 
 fclose(OUP);
 fprintf(1,'Output file %s created successfully. \n',NAME);
 end;
 end;