Last updated: 2023-03-16.

tf_quant_finance.math.pde.steppers.extrapolation.extrapolation_scheme

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Constructs extrapolation implicit-explicit scheme.

tf_quant_finance.math.pde.steppers.extrapolation.extrapolation_scheme(
    value_grid, t1, t2, equation_params_fn
)

Performs two implicit half-steps, one full implicit step, and combines them with such coefficients that ensure second-order errors. More computationally expensive than Crank-Nicolson scheme, but provides a better approximation for high-wavenumber components, which results in absence of oscillations typical for Crank-Nicolson scheme in case of non-smooth initial conditions. See [1] for details.

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

Args:

• value_grid: A Tensor of real dtype. Grid of solution values at the current time.

• t1: Time before the step.

• t2: Time after the step.

• equation_params_fn: A callable that takes a scalar Tensor argument representing time and constructs the tridiagonal matrix A (a tuple of three Tensors, main, upper, and lower diagonals) and the inhomogeneous term b. All of the Tensors are of the same dtype as inner_value_grid and of the shape broadcastable with the shape of inner_value_grid.

Returns:

A Tensor of the same shape and dtype a values_grid and represents an approximate solution u(t2).