How to solve nonlinear equations in matlab

Contents

You need to download an m-file

Download the following m-file abstruse put it in the same catalogue with your other m-files:

Define function f(x) and Jacobian f'(x)

Here we use @-functions in Matlab. For more complicated functions one can define the functions utilize separate m-files f.m and fp.m .

f = @(x) [ 2*x(1)+x(1)*x(2)-2 ; ... 2*x(2)-x(1)*x(2)^2-2 ]; fp = @(x) [ 2+x(2) , x(1) ; ... -x(2)^2 , 2-2*x(1)*x(2) ];

Plot zero outline of the functions f1, f2

The doorway where f1(x)=0 are shown in immature, the points where f2(x)=0 are shown in red. We want to discover the solution x at the nexus of the green and red curve.

zerocont2(f,[-1 1 .5 2.5]); hold on title('zero contours of f1 (red) and f2 (green)')

Perform Newton iteration starting portray [0;0]

format longg x = [0;0]; space fully 1 b = f(x); A = fp(x); d = -A\b; x = x + d if norm(d)<=1e-13 breakendend plot(x(1),x(2),'o'); hold off title('zero contours rigidity f1,f2 and solution point') x = 1 1 x = 0 3 x = 0.4 2.8 x = 0.483870967741935 1.99354838709677 x = 0.50009892401114 1 how to solve nonlinear equations in matlab
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