Split ODE Problems

# Split ODE Problems

## Mathematical Specification of a Split ODE Problem

To define a SplitODEProblem, you simply need to give a two functions functions $f_1$ and $f_2$ along with an initial condition $u₀$ which define an ODE:

$\frac{du}{dt} = f_1(u,p,t) + f_2(u,p,t)$

f should be specified as f(u,p,t) (or in-place as f(du,u,p,t)), 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.

Many splits are at least partially linear. That is the equation:

$\frac{du}{dt} = f_1(u,p,t) + f_2(u,p,t)$

For how to define a function as linear, see the documentation for the DiffEqOperators.

### Constructors

SplitODEProblem{isinplace}(f1,f2,u0,tspan;kwargs...)

### Fields

• f1, f2: The functions in the ODE.

• u0: The initial condition.

• tspan: The timespan for the problem.

• callback: A callback to be applied to every solver which uses the problem. Defaults to nothing.

• mass_matrix: The mass-matrix. Defaults to I, the UniformScaling identity matrix.