tf_quant_finance.math.pde.steppers.douglas_adi.douglas_adi_step

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Last updated: 2023-03-16.

tf_quant_finance.math.pde.steppers.douglas_adi.douglas_adi_step#

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Creates a stepper function with Crank-Nicolson time marching scheme.

tf_quant_finance.math.pde.steppers.douglas_adi.douglas_adi_step(
    theta=0.5
)

Douglas ADI scheme is the simplest time marching scheme for solving parabolic PDEs with multiple spatial dimensions. The time step consists of several substeps: the first one is fully explicit, and the following N steps are implicit with respect to contributions of one of the N axes (hence “ADI” - alternating direction implicit). See douglas_adi_scheme below for more details.

Args:#

  • theta: positive Number. theta = 0 corresponds to fully explicit scheme. The larger theta the stronger are the corrections by the implicit substeps. The recommended value is theta = 0.5, because the scheme is second order accurate in that case, unless mixed second derivative terms are present in the PDE.

Returns:#

Callable to be used in finite-difference PDE solvers (see fd_solvers.py).

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