Develop your own M-file function for the Newton- Raphson method for nonlinear systems of equations based on Fig. 12.4. Test it by solving Example 12.4 and then use it to solve Prob. 12.8.

Example 12.4

Data Form Problem 12.8

Determine the solution of the simultaneous nonlinear equations

y = −x² + x + 0.5
y + 5xy = x²

Use the Newton-Raphson method and employ initial guesses  of x = y = 1.2.

Transcribed Image Text:

function [x, f, ea, iter] =newtmult (func, xo, es, maxit, varargin) & newtmult: Newton-Raphson root zeroes nonlinear systems [x, f, ea, iter] =newtmult (func, xo, es, maxit, p1, p2, ...): 8 8 uses the Newton-Raphson method to find the roots of a system of nonlinear equations 8 & input: 8 func = name of function that returns f and J 8 xo initial guess es = desired percent relative error (default = 0.0001%) maxit = maximum allowable iterations (default = 50) p1, p2,... = additional parameters used by function & output: & & 8 8 f 8 & x = vector of roots f = vector of functions evaluated at roots ea = approximate percent relative error (%) iter = number of iterations if nargin<2, error (at least 2 input arguments required'), end if nargin<3|isempty (es), es=0.0001; end if nargin<4|isempty (maxit), maxit=50; end iter = 0; X=X0; while (1) [J, f]=func (x, varargin{:}); dx=J\f; x=x-dx; iter = iter + 1; ea=100*max (abs (dx./x)); if iter>=maxit | ea<=es, break, end end