# forward difference

## forward difference

[¦fȯr·wərd ′dif·rəns]
(mathematics)
One of a series of quantities obtained from a function whose values are known at a series of equally spaced points by repeatedly applying the forward difference operator to these values; used in interpolation or numerical calculation and integration of functions.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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We also take the forward difference scheme to the left boundary condition and the lower boundary condition.
We call [f.sup.[DELTA]](t) the delta (or Hilger) derivative of f(t) and it turns out that [f.sup.[DELTA]] is the usual derivative if T = R and is the usual forward difference operator if T = Z.
The forward difference operator is denoted by [DELTA].
In the transient term, we used the forward difference for
With the help of this method, we use backward space difference provided that the wave speed c is positive and if c is negative, we have to ensure the stability by using forward difference. For the above equation, may results as, at a grid point ( ) discussed within the region shown in fig.1.
[DELTA] is the first-order forward difference operator; that is, [DELTA]u(k) = u(k + 1) - u(k).
In a series of papers Villatoro and Ramos [4447] used the modified equation approach to analyze and improve the efficiency of an Euler forward difference method to solve linear and nonlinear differential equations.
where {p(n)}, [q(n)} are sequences of real numbers, {[sigma]a(n)} is a sequence of positive integers such that [sigma](n) > n + 1, ([tau](n)} is a nondecreasing sequence of nonnegative integers such that [tau](n) < n and [DELTA] is the forward difference operator defined by the equation [DELTA]x(n) = x(n + 1) - x(n).
The discrete-time analogue of the Lie derivative of a function ([phi](x) is its difference, which can be defined in two different ways, either as the forward difference
One can check that in these cases we have [f.sup.[DELTA]](t) = f'(t), [f.sup.[DELTA]](t) = [[DELTA].sub.[omega]] f(t) and [f.sup.[DELTA]](t) = [D.sub.q] f(t), respectively, where [[DELTA].sub.[omega]] f(t) = f (t + [omega]) - f(t) / [omega] is the forward difference operator with stepsize [omega] [32], and [D.sub.q] f(t) = f(qt) - f(t) / t(q - 1) (for t [not equal to] 0) is the q-difference operator [10].

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