sofia.pde.fdm.discretisation¶

sofia.pde.fdm.discretisation.as_finite_diff(expr, points=None, wrt=None, lhs=None, integer_stencils=None)¶

Compute a finite-difference approximation of a derivative.

This function returns a symbolic expression approximating a derivative of a function using a finite difference formula. The derivative is expressed as a weighted sum of the function evaluated at discrete points of the independent variable(s).

Parameters:

expr – The derivative to approximate.
points –
- If a sequence: the discrete values of the independent variable used to generate the finite difference weights (length >= order + 1).
- If a scalar: treated as the step size to generate an equidistant sequence of length order + 1 centered around x0.
- Default: 1 (unit step size).
lhs – Symbol of field representing the left-hand side, in which the result of the derivative is to be stored.
wrt – Variable with respect to which the derivative is taken. Required for partial derivatives if derivative is not ordinary. Default: None.
integer_stencils – Allows the use of optimised (integer stencils) or fall back to general stencils made from half-integer steps.

Returns:

Symbolic expression representing the finite-difference approximation of the derivative, as a weighted sum of the function evaluated at discrete points.

Return type:

sympy.Expr