All real roots of a nonlinear system of equations by three methods

Ideas
, , , ,
1
◔
1 Like
2

Have you tried comparing the results with the output of plain Solve?

f1[x_, y_, z1_] = x - y^2 Cos[y] z1;
f2[x_, y_, z2_] = -y + x Sin[x] + z2;
Solve[{f1[x, y, 7/10] == 0, f2[x, y, 1/10] == 0,
  Abs[x] <= 12, Abs[y] <= 12}, {x, y}, Reals]
1 Like
3

Hello,

you get the same roots with:

In[28]:= f1[x_, y_, z1_] = x - y^2 Cos[y] z1;
f2[x_, y_, z2_] = -y + x Sin[x] + z2;
NSolve[{f1[x, y, 7/10] == 0, f2[x, y, 1/10] == 0, Abs[x] <= 12, 
  Abs[y] <= 12.}, {x, y}, Reals]

Out[30]= {{x -> -11.7962, y -> -8.1129}, {x -> -11.2056, 
  y -> -10.8594}, {x -> -10.9669, y -> -10.8624}, {x -> -10.338, 
  y -> -8.08205}, {x -> -6.89791, y -> 4.07826}, {x -> -6.74497, 
  y -> 3.10517}, {x -> -5.73175, y -> -2.90294}, {x -> -5.31136, 
  y -> -4.28675}, {x -> -4.5359, y -> -4.36545}, {x -> -3.89694, 
  y -> -2.57153}, {x -> 0.00697177, y -> 0.100049}, {x -> 7.07058, 
  y -> 5.10964}, {x -> 7.68092, y -> 7.66617}, {x -> 8.27572, 
  y -> 7.6506}, {x -> 8.80764, y -> 5.197}, {x -> 9.99053, 
  y -> -5.25543}, {x -> 10.2718, y -> -7.5969}, {x -> 11.8655, 
  y -> -7.55223}}

However, NSolve will not work for any system of equations. Hence, the need for other tools.

1 Like