enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Finite difference - Wikipedia

    en.wikipedia.org/wiki/Finite_difference

    A finite difference is a mathematical expression of the form f (x + b) − f (x + a).If a finite difference is divided by b − a, one gets a difference quotient.The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems.

  3. Finite difference method - Wikipedia

    en.wikipedia.org/wiki/Finite_difference_method

    For example, consider the ordinary differential equation ′ = + The Euler method for solving this equation uses the finite difference quotient (+) ′ to approximate the differential equation by first substituting it for u'(x) then applying a little algebra (multiplying both sides by h, and then adding u(x) to both sides) to get (+) + (() +).

  4. Numerical methods for ordinary differential equations - Wikipedia

    en.wikipedia.org/wiki/Numerical_methods_for...

    and the second-order central difference for the second derivative is given by: + + = ″ + (). In both of these formulae, = is the distance between neighbouring x values on the discretized domain. One then constructs a linear system that can then be solved by standard matrix methods. For example, suppose the equation to be solved is:

  5. Five-point stencil - Wikipedia

    en.wikipedia.org/wiki/Five-point_stencil

    An illustration of the five-point stencil in one and two dimensions (top, and bottom, respectively). In numerical analysis, given a square grid in one or two dimensions, the five-point stencil of a point in the grid is a stencil made up of the point itself together with its four "neighbors".

  6. Numerical differentiation - Wikipedia

    en.wikipedia.org/wiki/Numerical_differentiation

    The classical finite-difference approximations for numerical differentiation are ill-conditioned. However, if is a holomorphic function, real-valued on the real line, which can be evaluated at points in the complex plane near , then there are stable methods.

  7. Nine-point stencil - Wikipedia

    en.wikipedia.org/wiki/Nine-point_stencil

    It is used to write finite difference approximations to derivatives at grid points. It is an example for numerical differentiation. This stencil is often used to approximate the Laplacian of a function of two variables. An illustration of the nine-point stencil in two dimensions.

  8. Second derivative - Wikipedia

    en.wikipedia.org/wiki/Second_derivative

    The second derivative of a function f can be used to determine the concavity of the graph of f. [2] A function whose second derivative is positive is said to be concave up (also referred to as convex), meaning that the tangent line near the point where it touches the function will lie below the graph of the function.

  9. Finite difference coefficient - Wikipedia

    en.wikipedia.org/wiki/Finite_difference_coefficient

    For example, the third derivative with a second-order accuracy is ... The theory of Lagrange polynomials provides explicit formulas for the finite difference ...