Solutions

Parallel Solution of a partitioned differential algebraic equation.

Serial Solution of a partitioned differential algebraic equation.

Create solution for partitioned DAE.

Create solution for ODE and split ODE.

Create solution for partitioned ODE.

Create solution for SDE.

Create solution for DAE.

Create solution for variational ODE.

Create solution for PSDE.

Print error for solutions of equations not implemented, yet.

Create solution for implicit DAE.

Create solution for implicit ODE.

Solution of a differential algebraic equation.

SolutionODE: Solution of an ordinary differential equation

Contains all fields necessary to store the solution of an ODE.

Fields

• nd: dimension of the dynamical variable $q$
• nt: number of time steps to store
• ni: number of initial conditions
• t: time steps
• q: solution q[nd, nt+1, ni] with q[:,0,:] the initial conditions
• ntime: number of time steps to compute
• nsave: save every nsave'th time step

Solution of a partitioned ordinary differential equation.

SolutionPSDE: Solution of a partitioned stochastic differential equation

Contains all fields necessary to store the solution of a PSDE or SPSDE

Fields

• conv: type of the solution: "strong" or "weak"
• nd: dimension of the dynamical variable $q$
• nm: dimension of the Wiener process
• nt: number of time steps to store
• ns: number of sample paths
• ni: number of initial conditions
• t: time steps
• q: solution q[nd, nt+1, ns, ni] with q[:,0,:,:] the initial conditions
• p: solution p[nd, nt+1, ns, ni] with p[:,0,:,:] the initial conditions
• W: Wiener process driving the stochastic processes q and p
• K: integer parameter defining the truncation of the increments of the Wiener process (for strong solutions),

•   A = √(2 K Δt |log Δt|) due to Milstein & Tretyakov; if K=0 no truncation

• ntime: number of time steps to compute
• nsave: save every nsave'th time step

SolutionSDE: Solution of a stochastic differential equation

Contains all fields necessary to store the solution of an SDE.

Fields

• conv: type of the solution: "strong" or "weak"
• nd: dimension of the dynamical variable $q$
• nm: dimension of the Wiener process
• nt: number of time steps to store
• ns: number of sample paths
• ni: number of initial conditions
• t: time steps
• q: solution q[nd, nt+1, ns, ni] with q[:,0,:,:] the initial conditions
• W: Wiener process driving the stochastic process q
• K: integer parameter defining the truncation of the increments of the Wiener process (for strong solutions),

•   A = √(2 K Δt |log Δt|) due to Milstein & Tretyakov; if K=0 no truncation

• ntime: number of time steps to compute
• nsave: save every nsave'th time step

Append solution to HDF5 file. offset - start writing q at the position offset+2 offset2- start writing ΔW, ΔZ at the position offset2+1

Append solution to HDF5 file. offset - start writing q at the position offset+2 offset2- start writing ΔW, ΔZ at the position offset2+1

Append solution to HDF5 file.

Append solution to HDF5 file.

Append solution to HDF5 file.

Append solution to HDF5 file.

Append solution to HDF5 file.

Append solution to HDF5 file.

Append solution to HDF5 file.

Append solution to HDF5 file.

Creates HDF5 file and initialises datasets for SDE solution object. It is implemented as one fucntion for all NQ and NW cases, rather than several separate cases as was done for SolutionODE. nt - the total number of time steps to store ntime - the total number of timesteps to be computed

Creates HDF5 file and initialises datasets for SDE solution object. It is implemented as one fucntion for all NQ and NW cases, rather than several separate cases as was done for SolutionODE. nt - the total number of time steps to store ntime - the total number of timesteps to be computed

Creates HDF5 file and initialises datasets for DAE solution object.

Creates HDF5 file and initialises datasets for DAE solution object.

Creates HDF5 file and initialises datasets for ODE solution object.

Creates HDF5 file and initialises datasets for ODE solution object.

Creates HDF5 file and initialises datasets for PDAE solution object with single initial condition.

Creates HDF5 file and initialises datasets for PDAE solution object with multiple initial conditions.

Creates HDF5 file and initialises datasets for PODE solution object.

Creates HDF5 file and initialises datasets for PODE solution object.

copies the m-th initial condition for the k-th sample path from sol.q to q

createHDF5: Creates or opens HDF5 file. A version for StochasticSolution. It does not create attributes and does not write the time array t, like the version above does. Instead these are set in create_hdf5(), so that arrays larger than currently held in the solution structure can be created in the file. In the future it would be better to rewrite the function above, so that it is universal for all solution structures.

createHDF5: Creates or opens HDF5 file.

Creates HDF5 file, writes solution to file, and closes file.