# Nonlinear Problems

SciMLBase.NonlinearProblemType

Defines a nonlinear system problem. Documentation Page: https://nonlinearsolve.sciml.ai/dev/basics/NonlinearProblem/

Mathematical Specification of a Nonlinear Problem

To define a Nonlinear Problem, you simply need to give the function $f$ which defines the nonlinear system:

$$$f(u,p) = 0$$$

and an initial guess $u₀$ of where f(u,p)=0. f should be specified as f(u,p) (or in-place as f(du,u,p)), and u₀ should be an AbstractArray (or number) whose geometry matches the desired geometry of u. Note that we are not limited to numbers or vectors for u₀; one is allowed to provide u₀ as arbitrary matrices / higher-dimension tensors as well.

Problem Type

Constructors

NonlinearProblem(f::NonlinearFunction,u0,p=NullParameters();kwargs...)
NonlinearProblem{isinplace}(f,u0,p=NullParameters();kwargs...)

isinplace optionally sets whether the function is in-place or not. This is determined automatically, but not inferred.

Parameters are optional, and if not given, then a NullParameters() singleton will be used, which will throw nice errors if you try to index non-existent parameters. Any extra keyword arguments are passed on to the solvers. For example, if you set a callback in the problem, then that callback will be added in every solve call.

For specifying Jacobians and mass matrices, see the NonlinearFunctions page.

Fields

• f: The function in the problem.
• u0: The initial guess for the steady state.
• p: The parameters for the problem. Defaults to NullParameters.
• kwargs: The keyword arguments passed on to the solvers.