tf_quant_finance.math.pde.steppers.weighted_implicit_explicit.weighted_implicit_explicit_step

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Last updated: 2023-03-16.

tf_quant_finance.math.pde.steppers.weighted_implicit_explicit.weighted_implicit_explicit_step#

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Creates a stepper function with weighted implicit-explicit scheme.

tf_quant_finance.math.pde.steppers.weighted_implicit_explicit.weighted_implicit_explicit_step(
    theta
)

Given a space-discretized equation

du/dt = A(t) u(t) + b(t)

(here u is a value vector, A and b are the matrix and the vector defined by the PDE), the scheme approximates the right-hand side as a weighted average of values taken before and after a time step:

(u(t2) - u(t1)) / (t2 - t1) = theta * (A(t1) u(t1) + b(t1))
   + (1 - theta) (A(t2) u(t2) + b(t2)).

Includes as particular cases the implicit (theta = 0), explicit (theta = 1), and Crank-Nicolson (theta = 0.5) schemes.

The scheme is stable for theta >= 0.5, is second order accurate if theta = 0.5 (i.e. in Crank-Nicolson case), and first order accurate otherwise.

More details can be found in weighted_implicit_explicit_scheme below.

Args:#

  • theta: A float in range [0, 1]. A parameter used to mix implicit and explicit schemes together. Value of 0.0 corresponds to the fully implicit scheme, 1.0 to the fully explicit, and 0.5 to the Crank-Nicolson scheme.

Returns:#

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

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