Take one timestep of an implicit solver for a given instrument

1 2 3 4 | ```
take_implicit_timestep(t, S, full_discount_factor, local_discount_factor,
discount_factor_fcn, prev_grid_values, survival_probabilities,
tridiag_matrix_entries, instrument = NULL, dividends = NULL,
instr_name = "this instrument")
``` |

`t` |
Time after this timestep has been taken |

`S` |
Underlying equity values for the grid |

`full_discount_factor` |
A discount factor for the transform from grid values to actual derivative prices |

`local_discount_factor` |
A discount factor to apply to recovery values |

`discount_factor_fcn` |
A function for computing present values to
time |

`prev_grid_values` |
A vector of space grid values from the previously calculated timestep |

`survival_probabilities` |
Vector of probabilities of survival for each space grid node |

`tridiag_matrix_entries` |
Diagonal, superdiagonal and subdiagonal of tridiagonal matrix from the numerical integrator |

`instrument` |
If not NULL/NA, must have a |

`dividends` |
A |

`instr_name` |
Name of instrument to use in log messages |

Grid values for the instrument after taking the implicit timestep

Other Implicit Grid Solver: `construct_implicit_grid_structure`

,
`find_present_value`

,
`form_present_value_grid`

,
`infer_conforming_time_grid`

,
`integrate_pde`

,
`iterate_grid_from_timestep`

,
`timestep_instruments`

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