*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.
```python
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).