finite difference

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finite difference

[¦fī‚nīt ′dif·rəns]
(mathematics)
The difference between the values of a function at two discrete points, used to approximate the derivative of the function.
References in periodicals archive ?
Taking the forward time central space technique [15] into (5), we get the following finite difference equation:
The finite difference equation of the second term, [K.sub.[theta]][partial derivative][h.sup.*]/[partial derivative]z in Eq.
Substituting (7), (10), and (13) into (14) and replacing [u.sub.m+i,n+j] with [U.sub.m+i,n+j] (i, j [member of] [Z.sub.2]) yield the 25-point finite difference equation
Although the use of a uniform grid system, like that shown in Figure 2, greatly simplifies the finite difference equations and cell-to-cell relationships, it is computationally inefficient.
In fact the essence of the method of differences for the solution of differential equations is that instead of solving a differential equation one solves a corresponding finite difference equation that is obtained by substituting differences expressions with higher or lower level of accuracy for the derivatives.
Finite difference inequalities which exhibit explicit bounds on unknown functions in general provide a very useful and important tool in the development of the theory of finite difference equations. Due to the fact that finite difference inequalities have been applied in various branches of finite difference equations, many such inequalities with in one or two variables have been established [1-4].
Richtmyer, Survey of the stability of linear finite difference equations, Comm.
Richtmyer, "Survey of the stability of linear finite difference equations," Communications on Pure and Applied Mathematics, vol.
One idea is to replace the derivatives appearing in the partial differential equation by finite difference equations that approximate them.
Centered differencing at point (i' k) is achieved on these equations, leading to finite difference equations

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