math::differentiation::numeric_3D::central_difference Namespace Reference

Functions
auto	partialX (auto f, const auto x, const auto y, const auto t)
	Approximates the partial derivative ∂f/∂x of a function f(x, y, t) using central differences.
auto	partialY (auto f, const auto x, const auto y, const auto t)
	Approximates the partial derivative ∂f/∂y of a function f(x, y, t) using central differences.
auto	partialT (auto f, const auto x, const auto y, const auto t)
	Approximates the partial derivative ∂f/∂t of a function f(x, y, t) using central differences.

Function Documentation

partialT()

auto math::differentiation::numeric_3D::central_difference::partialT	(	auto	f,
		const auto	x,
		const auto	y,
		const auto	t )

Approximates the partial derivative ∂f/∂t of a function f(x, y, t) using central differences.

This lambda computes the numerical derivative of a scalar function with respect to the t-direction via a second-order central difference scheme. The step size is adaptively chosen based on machine precision to balance truncation and rounding errors.

Parameters

f	The function to differentiate; must accept (x, y, t) as input
x	The x-coordinate (passed to f but not differentiated)
y	The y-coordinate (passed to f but not differentiated)
t	The time value at which the derivative is evaluated

Returns

Approximation of ∂f/∂t at (x, y, t)

Definition at line 55 of file CentralDifferencePartial2D.h.

partialX()

auto math::differentiation::numeric_3D::central_difference::partialX	(	auto	f,
		const auto	x,
		const auto	y,
		const auto	t )

Approximates the partial derivative ∂f/∂x of a function f(x, y, t) using central differences.

This lambda computes the numerical derivative of a scalar function with respect to the x-direction via a second-order central difference scheme. The step size is adaptively chosen based on machine precision to balance truncation and rounding errors.

Parameters

f	The function to differentiate; must accept (x, y, t) as input
x	The x-coordinate at which the derivative is evaluated
y	The y-coordinate (passed to f but not differentiated)
t	The time value (passed to f but not differentiated)

Returns

Approximation of ∂f/∂x at (x, y, t)

Definition at line 19 of file CentralDifferencePartial2D.h.

partialY()

auto math::differentiation::numeric_3D::central_difference::partialY	(	auto	f,
		const auto	x,
		const auto	y,
		const auto	t )

Approximates the partial derivative ∂f/∂y of a function f(x, y, t) using central differences.

This lambda computes the numerical derivative of a scalar function with respect to the y-direction via a second-order central difference scheme. The step size is adaptively chosen based on machine precision to balance truncation and rounding errors.

Parameters

f	The function to differentiate; must accept (x, y, t) as input
x	The x-coordinate (passed to f but not differentiated)
y	The y-coordinate at which the derivative is evaluated
t	The time value (passed to f but not differentiated)

Returns

Approximation of ∂f/∂y at (x, y, t)

Definition at line 37 of file CentralDifferencePartial2D.h.