Finite Difference Algorithm, Boudary Value Problem-Numerical Analysis-MATLAB Code, Exercises of Mathematical Methods for Numerical Analysis and Optimization

% NONLINEAR FINITE-DIFFERENCE ALGORITHM 11.4

%

% To approximate the solution to 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;

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

%

syms('VMAX', 'J', 'x', 'y', 'z', 's');

TRUE = 1;

FALSE = 0;

fprintf(1,'This is the Nonlinear Finite-Difference 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 \n');

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

fprintf(1,'to z = y-prime on the third line. \n');

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

fprintf(1,' -z/8 \n');

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

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;

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');