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

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Muzammil Arif
Muzammil Arif el 13 de Mzo. de 2021
Comentada: Sergey Kasyanov el 15 de Mzo. de 2021
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).

Respuestas (1)

Sergey Kasyanov
Sergey Kasyanov el 13 de Mzo. de 2021
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);
  3 comentarios
Muzammil Arif
Muzammil Arif el 14 de Mzo. de 2021
0.5 and - 0.3 are the answer by solving
Sergey Kasyanov
Sergey Kasyanov el 15 de Mzo. de 2021
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].

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