OOF2: The Manual
Newton (Newton) — Solve nonlinear equations with Newton's method.
- Relative tolerance for convergence to a nonlinear solution. Type: A real number.
- Absolute tolerance for convergence to a nonlinear solution. Type: A real number.
- Maximum number of iterations for convergence to a nonlinear solution. Type: Integer.
It implements Newton's method, which uses the derivative
of the nonlinear term with respect to the vector
Field values), to compute
successive approximations to the solution. The iteration stops when
the norm of the residual after the
or when the
maximum_iterations limit is exceeded.
Newton's method generally converges in fewer iterations than Picard, but may require more work per iteration.
Newton's method relies upon knowing the derivatives of the nonlinear
function with respect to the unknowns, . This information comes from the
Properties, which determine the exact form of the
equations being solved. Nonlinear
Properties that are built into
OOF2 provide routines to compute the derivatives, but
defined in OOF2 extensions might not. In this
Newton will compute the derivatives
numerically. This will make
more computations on each iteration and quite possibly also require
more iterations. The parameters used for the numerical
differentiation may be set by the OOF.Settings.Mesh_Defaults.Numerical_Differentiation