tf_quant_finance.math.pde.boundary_conditions.neumann

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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.

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).

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:

@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.

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