Can anyone help me solve this problem using Newton's Method?

Using Newton's Method solve the equations:

x^3 + y^2 + x - 0.715 = 0
x^2 + y^3 - y - 0.523 = 0

with (x0, y0) = (1, 0).

Answer 1

[Sergey Kasyanov]

Hello,

try that

i = 1;
V0 = [1;0];%[x0;y0]
V = V0 + 1;
while max(abs(V0 - V)) > 1e-10 && i < 1e2
    V = V0;
    J = [3*V(1)^2+1   2*V(2)
         2*V(1)       3*V(2)^2-1];
    F = [V(1)^3+V(2)^2+V(1)-0.715
        V(1)^2+V(2)^3-V(2)-0.523];
    V0 = V - F./(J*V);
    i = i + 1;
end
x = V(1);
y = V(2);

[Muzammil Arif]

There is no error in the code but the answer are not matching with what i have done by hand

[Muzammil Arif]

0.5 and - 0.3 are the answer by solving

[Sergey Kasyanov]

There are some solutions of the equations system. You can try to find another solutions by changing start point or by adding and varying coefficient k in equation (0<k<1):

V0 = V - k * F./(J*V);

There are three solution near the 0: [-0.46, 1.13], [0.38;-0.54], [0.5;-0.3].