*Last updated: 2023-03-16.*
# tf_quant_finance.math.pde.boundary_conditions.neumann
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Wrapper for Neumann boundary condition to be used in PDE solvers.
```python
tf_quant_finance.math.pde.boundary_conditions.neumann(
boundary_normal_derivative_fn
)
```
Example: the normal boundary derivative is 1 on both boundaries (i.e.
`dV/dx = 1` on upper boundary, `dV/dx = -1` on lower boundary).
```python
def lower_boundary_fn(t, location_grid):
return 1
def upper_boundary_fn(t, location_grid):
return 1
solver = fd_solvers.step_back(...,
boundary_conditions = [(neumann(lower_boundary_fn),
neumann(upper_boundary_fn))],
...)
```
Also can be used as a decorator:
```python
@neumann
def lower_boundary_fn(t, location_grid):
return 1
@neumann
def upper_boundary_fn(t, location_grid):
return 1
solver = fd_solvers.solve_forward(...,
boundary_conditions = [(lower_boundary_fn, upper_boundary_fn)],
...)
```
#### Args:
* `boundary_normal_derivative_fn`: Callable returning the values of the
derivative with respect to the exterior normal to the boundary at the
given time.
Accepts two arguments - the moment of time and the current coordinate
grid.
Returns a number, a zero-rank Tensor or a Tensor of shape
`batch_shape + grid_shape'`, where `grid_shape'` is grid_shape excluding
the axis orthogonal to the boundary. For example, in 3D the value grid
shape is `batch_shape + (z_size, y_size, x_size)`, and the boundary
tensors on the planes `y = y_min` and `y = y_max` should be either scalars
or have shape `batch_shape + (z_size, x_size)`. In 1D case this reduces
to just `batch_shape`.
#### Returns:
Callable suitable for PDE solvers.