How can I solve a nonlinear model using Newton Raphson ?

Hi

How can I solve this nonlinear model using Newton Raphson ?

x1 +x2^2 +cos (x3) = 2
x1 +sin (x2) + x3^3 = 1
x3 +x2^3+x3^3 = 4

Answer 1

[Stephan]

One way:

result = fsolve(@fun,[1 1 1])

function F = fun(x)
F(1) = x(1) + x(2).^2 + cos(x(3)) - 2;
F(2) = x(1) + sin(x(2)) + x(3).^3 - 1;
F(3) = x(3) +x(2).^3 + x(3).^3 - 4;
end

gives:

Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.

<stopping criteria details>

result =

   -0.5583    1.3732    0.8329

[John D'Errico]

The best way to solve it. Don't use Newton-Raphson at all. :)

[Mallouli Marwa]

If I want to use Newton Raphson.

How can we change it ?