Base Solvers

class pybamm.BaseSolver(method=None, tol=1e-08)

Solve a discretised model.

Parameters:tolerance (float, optional) – The tolerance for the solver (default is 1e-8).

compute_solution(model, t_eval)

Calculate the solution of the model at specified times. Note: this does not execute the solver setup.

Parameters:

• model (pybamm.BaseModel) – The model whose solution to calculate. Must have attributes rhs and initial_conditions
• t_eval (numeric type) – The times at which to compute the solution

get_termination_reason(solution, events)

Identify the cause for termination. In particular, if the solver terminated due to an event, (try to) pinpoint which event was responsible. Note that the current approach (evaluating all the events and then finding which one is smallest at the final timestep) is pretty crude, but is the easiest one that works for all the different solvers.

Parameters:

• solution (pybamm.Solution) – The solution object
• events (dict) – Dictionary of events

set_up(model)

Unpack model, perform checks, simplify and calculate jacobian.

Parameters:model (pybamm.BaseModel) – The model whose solution to calculate. Must have attributes rhs and initial_conditions Raises:pybamm.SolverError – If the model contains any algebraic equations (in which case a DAE solver should be used instead)

solve(model, t_eval)

Execute the solver setup and calculate the solution of the model at specified times.

Parameters:

• model (pybamm.BaseModel) – The model whose solution to calculate. Must have attributes rhs and initial_conditions
• t_eval (numeric type) – The times at which to compute the solution

Raises:

pybamm.ModelError – If an empty model is passed (model.rhs = {} and model.algebraic={})

step(model, dt, npts=2)

Step the solution of the model forward by a given time increment. The first time this method is called it executes the necessary setup by calling self.set_up(model).

Parameters:

• model (pybamm.BaseModel) – The model whose solution to calculate. Must have attributes rhs and initial_conditions
• dt (numeric type) – The timestep over which to step the solution
• npts (int, optional) – The number of points at which the solution will be returned during the step dt. default is 2 (returns the solution at t0 and t0 + dt).

Raises:

pybamm.ModelError – If an empty model is passed (model.rhs = {} and model.algebraic={})

class pybamm.OdeSolver(method=None, tol=1e-08)

Solve a discretised model.

Parameters:tolerance (float, optional) – The tolerance for the solver (default is 1e-8).

compute_solution(model, t_eval)

Calculate the solution of the model at specified times.

Parameters:

• model (pybamm.BaseModel) – The model whose solution to calculate. Must have attributes rhs and initial_conditions
• t_eval (numeric type) – The times at which to compute the solution

integrate(derivs, y0, t_eval, events=None, mass_matrix=None, jacobian=None)

Solve a model defined by dydt with initial conditions y0.

Parameters:

• derivs (method) – A function that takes in t and y and returns the time-derivative dydt
• y0 (numeric type) – The initial conditions
• t_eval (numeric type) – The times at which to compute the solution
• events (method, optional) – A function that takes in t and y and returns conditions for the solver to stop
• mass_matrix (array_like, optional) – The (sparse) mass matrix for the chosen spatial method.
• jacobian (method, optional) – A function that takes in t and y and returns the Jacobian

set_up(model)

Unpack model, perform checks, simplify and calculate jacobian.

Parameters:model (pybamm.BaseModel) – The model whose solution to calculate. Must have attributes rhs and initial_conditions Raises:pybamm.SolverError – If the model contains any algebraic equations (in which case a DAE solver should be used instead)

class pybamm.DaeSolver(method=None, tol=1e-08, root_method='lm', root_tol=1e-06, max_steps=1000)

Solve a discretised model.

Parameters:

• tolerance (float, optional) – The tolerance for the solver (default is 1e-8).
• root_method (str, optional) – The method to use to find initial conditions (default is “lm”)
• tolerance – The tolerance for the initial-condition solver (default is 1e-8).
• max_steps (int, optional) – The maximum number of steps the solver will take before terminating (default is 1000).

calculate_consistent_initial_conditions(rhs, algebraic, y0_guess, jac=None)

Calculate consistent initial conditions for the algebraic equations through root-finding

Parameters:

• rhs (method) – Function that takes in t and y and returns the value of the differential equations
• algebraic (method) – Function that takes in t and y and returns the value of the algebraic equations
• y0_guess (array-like) – Array of the user’s guess for the initial conditions, used to initialise the root finding algorithm
• jac (method) – Function that takes in t and y and returns the value of the jacobian for the algebraic equations

Returns:

y0_consistent – Initial conditions that are consistent with the algebraic equations (roots of the algebraic equations)

Return type:

array-like, same shape as y0_guess

compute_solution(model, t_eval)

Calculate the solution of the model at specified times.

Parameters:

• model (pybamm.BaseModel) – The model whose solution to calculate. Must have attributes rhs and initial_conditions
• t_eval (numeric type) – The times at which to compute the solution

integrate(residuals, y0, t_eval, events=None, mass_matrix=None, jacobian=None)

Solve a DAE model defined by residuals with initial conditions y0.

Parameters:

• residuals (method) – A function that takes in t, y and ydot and returns the residuals of the equations
• y0 (numeric type) – The initial conditions
• t_eval (numeric type) – The times at which to compute the solution
• events (method, optional) – A function that takes in t and y and returns conditions for the solver to stop
• mass_matrix (array_like, optional) – The (sparse) mass matrix for the chosen spatial method.
• jacobian (method, optional) – A function that takes in t, y and ydot and returns the Jacobian

set_up(model)

Unpack model, perform checks, simplify and calculate jacobian.

Parameters:model (pybamm.BaseModel) – The model whose solution to calculate. Must have attributes rhs and initial_conditions Raises:pybamm.SolverError – If the model contains any algebraic equations (in which case a DAE solver should be used instead)