|
1 | 1 | # Nonlinear Problems
|
2 | 2 |
|
3 |
| -## Mathematical Specification of a Nonlinear Problem |
4 |
| - |
5 |
| -To define a Nonlinear Problem, you simply need to give the function ``f`` |
6 |
| -which defines the nonlinear system: |
7 |
| - |
8 |
| -```math |
9 |
| -f(u,p) = 0 |
10 |
| -``` |
11 |
| - |
12 |
| -and an initial guess ``u₀`` of where `f(u,p)=0`. `f` should be specified as `f(u,p)` |
13 |
| -(or in-place as `f(du,u,p)`), and `u₀` should be an AbstractArray (or number) |
14 |
| -whose geometry matches the desired geometry of `u`. Note that we are not limited |
15 |
| -to numbers or vectors for `u₀`; one is allowed to provide `u₀` as arbitrary |
16 |
| -matrices / higher-dimension tensors as well. |
17 |
| - |
18 |
| -## Problem Type |
19 |
| - |
20 |
| -### Constructors |
21 |
| - |
22 |
| -```julia |
23 |
| -NonlinearProblem(f::NonlinearFunction,u0,p=NullParameters();kwargs...) |
24 |
| -NonlinearProblem{isinplace}(f,u0,p=NullParameters();kwargs...) |
25 |
| -``` |
26 |
| - |
27 |
| -`isinplace` optionally sets whether the function is in-place or not. This is |
28 |
| -determined automatically, but not inferred. |
29 |
| - |
30 |
| -Parameters are optional, and if not given, then a `NullParameters()` singleton |
31 |
| -will be used, which will throw nice errors if you try to index non-existent |
32 |
| -parameters. Any extra keyword arguments are passed on to the solvers. For example, |
33 |
| -if you set a `callback` in the problem, then that `callback` will be added in |
34 |
| -every solve call. |
35 |
| - |
36 |
| -For specifying Jacobians and mass matrices, see the [NonlinearFunctions](@ref nonlinearfunctions) |
37 |
| -page. |
38 |
| - |
39 |
| -### Fields |
40 |
| - |
41 |
| -* `f`: The function in the problem. |
42 |
| -* `u0`: The initial guess for the steady state. |
43 |
| -* `p`: The parameters for the problem. Defaults to `NullParameters`. |
44 |
| -* `kwargs`: The keyword arguments passed on to the solvers. |
| 3 | +```@docs |
| 4 | +NonlinearProblem |
| 5 | +``` |
0 commit comments