Non Linear Shooting Algorithm Boundary Value Problem-Numerical Analysis-MATLAB Code, Exercises of Mathematical Methods for Numerical Analysis and Optimization

% NONLINEAR SHOOTING ALGORITHM 11.2

%

% To approximate the solution of the nonlinear boundary-value problem

%

% Y'' = F(X,Y,Y'), A<=X<=B, Y(A) = ALPHA, Y(B) = BETA:

%

%

% INPUT: Endpoints A,B; boundary conditions ALPHA, BETA; number of

% subintervals N; tolerance TOL; maximum number of iterations M.

syms('W2', 'U1', 'U2', 'I', 'X', 'T', 'K11', 'K12', 'K21');

syms('K22', 'K31', 'K32', 'K41', 'K42', 'J', 's', 'x', 'y', 'z');

TRUE = 1;

FALSE = 0;

fprintf(1,'This is the Nonlinear Shooting Method.\n');

fprintf(1,'Input the function F(X,Y,Z) in terms of x, y, z.\n');

fprintf(1,'followed by the partial of F with respect to y on the \n');

fprintf(1,'next line followed by the partial of F with respect to \n');

fprintf(1,'z or y-prime on the next line. \n');

fprintf(1,'For example: (32+2*x^3-y*z)/8 \n');

s = input(' ','s');

FYP = inline(s,'x','y','z');

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;

TK = (BETA-ALPHA)/(B-A);

fprintf(1,'TK = %.8e\n', TK);

fprintf(1,'Input new TK? Enter Y or N.\n');

AA = input(' ','s');

if AA == 'Y' | AA == 'y'

fprintf(1,'input new TK\n');

TK = input(' ');