% CONTINUATION METHOD FOR SYSTEMS ALGORITHM 10.1
%
% To approximate the solution of the nonlinear system F(X)=0 given
% an initial approximation X:
%
% INPUT: Number n of equations and unknowns; initial approximation
% X=(X(1),...,X(n)); number of RK4 steps N.
%
% OUTPUT: Approximate solution X=(X(1),...,X(n)) or a message
% that the number of iterations was exceeded.
syms('OK', 'N', 'I', 'J', 'P', 'NN', 'X','ZZ');
syms('FLAG', 'NAME', 'OUP', 'K', 'A', 's', 'ss','mm');
syms('KK1', 'I1', 'Z1', 'IR1', 'IA1', 'J1', 'C1', 'L1', 'JA1');
syms('K1','K2','K3','K4','X1','KK','H','b');
TRUE = 1;
FALSE = 0;
fprintf(1,'This is the Continuation Method for Nonlinear Systems.\n');
fprintf(1,'The functions could be input or defined in code.\n');
fprintf(1,'This code assumes input of functions - see \n');
fprintf(1,'comments in code for alternate version.\n');
fprintf(1,'This program also uses M-files JAC.M and FN.M \n');
fprintf(1,'If the number of equations exceeds 7 then JAC.M\n');
fprintf(1,'and FN.M must be changed.\n');
OK = FALSE;
while OK == FALSE
fprintf(1,'Input the number n of equations.\n');
N = input(' ');
if N >= 2
OK = TRUE;
else
fprintf(1,'N must be an integer greater than 1.\n');
end;
end;
A = zeros(N,N+1);
K1 = zeros(4,N);
X = zeros(1,N);
Y = zeros(1,N);
X1 = zeros(1,N);
b = zeros(1,N);
mm = zeros(1,4);
mm(1) = 0.5;
mm(2) = 0.5;
mm(3) = 1.0;
mm(4) = 0;
% Define components of F as follows:
s(1) = '3*y1-cos(y2*y3)-0.5';
s(2) = 'y1^2-81*(y2+0.1)^2+sin(y3)+1.06';
s(3) = 'exp(-y1*y2)+20*y3+(10*pi-3)/3';
% for I = 1 : N
% fprintf(1,'Input the function F_(%d) in terms of y1 ... y%d \n' ,I ,N);
% s(I) = input(' ','s');
% end;
% for I = 1 : N
% for J = 1 : N
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