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FindRoot::dfmin

FindRoot::dfmin

Details

  • This message comes up when nonlinear system of equations has reached the minimal damping factor allowed and is then unable to solve the equations.
  • For the case of nonlinear partial differential equations, an "InitialSeeding" can be specified to use a seed different than the default starting seed.
  • Off[message] switches off the message; On[message] switches it on. For example: Off[FindRoot::dfmin].

Examples

Basic Examples  (1)

Consider this nonlinear PDE:

Wolfram Language code: eq = Laplacian[u[x, y], {x, y}] == -(1 + y / (x ^ 2 + y ^ 2)) * u[x, y] + u[x, y] ^ 3; dC = DirichletCondition[u[x, y] == 1, True]; NDSolveValue[{eq, dC}, u[x, y], {x, y}∈Disk[{0, 0}, 10]]

A way to find an initial seed is to solve a related linear problem by removing at least the nonlinear terms. In this case, some linear terms have also been removed:

Wolfram Language code: initalSeed = NDSolveValue[{Laplacian[u[x, y], {x, y}] == 0, dC}, u[x, y], {x, y}∈Disk[{0, 0}, 10]]; Plot3D[initalSeed, {x, y}∈Disk[{0, 0}, 10]]

This initial seed can now be used to solve the nonlinear PDE:

Wolfram Language code: nds = NDSolveValue[{eq, dC}, u, {x, y}∈Disk[{0, 0}, 10], InitialSeeding -> u[x, y] == initalSeed]; Plot3D[nds[x, y], {x, y}∈Disk[{0, 0}, 10]]