*Last updated: 2023-03-16.*
# tf_quant_finance.math.pde.steppers.extrapolation.extrapolation_scheme
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Constructs extrapolation implicit-explicit scheme.
```python
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 `Tensor`s, main, upper, and lower diagonals)
and the inhomogeneous term `b`. All of the `Tensor`s 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)`.