equations= Flatten[stepCol3];
Length[stepCol6]
25
unknowns = Union[Cases[Level[equations, -1], u[x, y] -> u[x, y]]]
{u[-2., -2.], u[-2., -1.], u[-2., 0.], u[-2., 1.], u[-2., 2.],
u[-1., -2.], u[-1., -1.], u[-1., 0.], u[-1., 1.], u[-1., 2.],
u[0., -2.], u[0., -1.], u[0., 0.], u[0., 1.], u[0., 2.], u[1., -2.],
u[1., -1.], u[1., 0.], u[1., 1.], u[1., 2.], u[2., -2.], u[2., -1.],
u[2., 0.], u[2., 1.], u[2., 2.]}
Length[unknowns]
25
intialpts = RandomReal[1, Length[unknowns]]
{0.250597, 0.299283, 0.182427, 0.723877, 0.0188032, 0.72179, \
0.252471, 0.829026, 0.654356, 0.891575, 0.935469, 0.68797, 0.202407, \
0.00774897, 0.708065, 0.983459, 0.549046, 0.802898, 0.969589, \
0.769259, 0.0190204, 0.959561, 0.421826, 0.745957, 0.367205}
Length[intialpts]
25
sol = FindRoot[equations, Transpose[{unknowns, intialpts}],
MaxIterations -> 500]
FindRoot::jsing: Encountered a singular Jacobian at the point {u[-2.,-2.],u[-2.,-1.],u[-2.,0.],u[-2.,1.],u[-2.,2.],u[-1.,-2.],u[-1.,-1.],u[-1.,0.],u[-1.,1.],<<7>>,u[1.,-1.],u[1.,0.],u[1.,1.],u[1.,2.],u[2.,-2.],u[2.,-1.],u[2.,0.],u[2.,1.],u[2.,2.]} = {0.250597,0.299283,0.182427,0.723877,0.0188032,<<15>>,0.0190204,0.959561,0.421826,0.745957,0.367205}. Try perturbing the initial point(s). >>
