NonlinearSystem

struct NonlinearSystem <: AbstractTimeIndependentSystem

A nonlinear system of equations.

Fields

• eqs

  Vector of equations defining the system.

• states

  Unknown variables.

• ps

  Parameters.

• var_to_name

  Array variables.

• observed

• jac

  Jacobian matrix. Note: this field will not be defined until calculate_jacobian is called on the system.

• name

  Name: the name of the system. These are required to have unique names.

• systems

  systems: The internal systems

• defaults

  defaults: The default values to use when initial conditions and/or parameters are not supplied in ODEProblem.

• connector_type

  type: type of the system

• connections

  connections: connections in a system

• tearing_state

  tearing_state: cache for intermediate tearing state

• substitutions

  substitutions: substitutions generated by tearing.

Examples

@variables x y z
@parameters σ ρ β

eqs = [0 ~ σ*(y-x),
       0 ~ x*(ρ-z)-y,
       0 ~ x*y - β*z]
@named ns = NonlinearSystem(eqs, [x,y,z],[σ,ρ,β])

tearing(sys; simplify=false)

Tear the nonlinear equations in system. When simplify=true, we simplify the new residual residual equations after tearing. End users are encouraged to call structural_simplify instead, which calls this function internally.

function DiffEqBase.NonlinearProblem{iip}(sys::NonlinearSystem,u0map,
                                          parammap=DiffEqBase.NullParameters();
                                          jac = false, sparse=false,
                                          checkbounds = false,
                                          linenumbers = true, parallel=SerialForm(),
                                          kwargs...) where iip

Generates an NonlinearProblem from a NonlinearSystem and allows for automatically symbolically calculating numerical enhancements.