tf_quant_finance.math.pde.steppers.oscillation_damped_crank_nicolson.oscillation_damped_crank_nicolson_step

Last updated: 2023-03-16.

tf_quant_finance.math.pde.steppers.oscillation_damped_crank_nicolson.oscillation_damped_crank_nicolson_step#

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Scheme similar to Crank-Nicolson, but ensuring damping of oscillations.

tf_quant_finance.math.pde.steppers.oscillation_damped_crank_nicolson.oscillation_damped_crank_nicolson_step(
    extrapolation_steps=1
)

Performs first (or first few) steps with Extrapolation scheme, then proceeds with Crank-Nicolson scheme. This combines absence of oscillations by virtue of Extrapolation scheme with lower computational cost of Crank-Nicolson scheme.

See [1], [2] ([2] mostly discusses using fully implicit scheme on the first step, but mentions using extrapolation scheme for better accuracy in the end).

References:#

[1]: D. Lawson, J & Ll Morris, J. The Extrapolation of First Order Methods for Parabolic Partial Differential Equations. I. 1978 SIAM Journal on Numerical Analysis. 15. 1212-1224. https://epubs.siam.org/doi/abs/10.1137/0715082 [2]: B. Giles, Michael & Carter, Rebecca. Convergence analysis of Crank-Nicolson and Rannacher time-marching. J. Comput. Finance. 9. 2005. https://core.ac.uk/download/pdf/1633712.pdf

Args:#

  • extrapolation_steps: number of first steps to which to apply the Extrapolation scheme. Defaults to 1.

Returns:#

Callable to use as one_step_fn in fd_solvers.

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