OOF2: The Manual
Name
Picard (Picard) — Solve nonlinear equations with Picard iteration. Picard converges more slowly than Newton's method, but does less work per iteration.
Synopsis
Picard
(relative_tolerance
,absolute_tolerance
,maximum_iterations
)
Details

Base class:
NonlinearSolverBase

Parameters:
relative_tolerance
 Relative tolerance for convergence to a nonlinear solution. Type: A real number.
absolute_tolerance
 Absolute tolerance for convergence to a nonlinear solution. Type: A real number.
maximum_iterations
 Maximum number of iterations for convergence to a nonlinear solution. Type: Integer.
Description
Picard
is a nonlinear
solver used in AdvancedSolverMode for solving nonlinear
equations by Picard iteration.
Given equations of the form
where is a vector of unknowns
(Field
values), is a nonlinear
matrixvalued function of , and is a vector, and a
trial solution , the next trial
solution is obtained by solving
Picard
iterates this procedure until the
residual, satisfies
where =relative_tolerance
and =absolute_tolerance
,
or when the maximum_iterations
limit is exceeded.
Note  

We've written equation (6.152), which is
being solved by 