Finite Difference - Finite Difference in Several Variables

Finite Difference in Several Variables

Finite differences can be considered in more than one variable. They are analogous to partial derivatives in several variables.

Some partial derivative approximations are:

Alternatively, for applications in which the computation of is the most costly step and both first and second derivatives must be computed, a more efficient formula for the last case is:

since the only values to be computed which are not already needed for the previous four equations are and .

Read more about this topic:  Finite Difference

Famous quotes containing the words finite, difference and/or variables:

    Sisters define their rivalry in terms of competition for the gold cup of parental love. It is never perceived as a cup which runneth over, rather a finite vessel from which the more one sister drinks, the less is left for the others.
    Elizabeth Fishel (20th century)

    That was always the difference between Muhammad Ali and the rest of us. He came, he saw, and if he didn’t entirely conquer—he came as close as anybody we are likely to see in the lifetime of this doomed generation.
    Hunter S. Thompson (b. 1939)

    Science is feasible when the variables are few and can be enumerated; when their combinations are distinct and clear. We are tending toward the condition of science and aspiring to do it. The artist works out his own formulas; the interest of science lies in the art of making science.
    Paul Valéry (1871–1945)