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 ?
There are finite difference techniques, such as Newton's advancing difference formula, that use more data from the difference table to ascertain the quadratic function, but alas they require more time to master and employ some tertiary level mathematics.
In [11], a better finite difference scheme to solve the dynamic one-dimensional advection-dispersion-reaction equations (ADRE) is focused upon, and the effect of non-uniform water flows in a stream is considered.
2 Transformed problem and iterative finite difference solution
The computed solutions can then be refined by the finite element method or the finite difference method.
In Section 3, the finite difference schemes for the computation approach are introduced.
The characteristic finite difference (CFD) scheme of the pollutant transport model (1) is given as
In this section, we present some new and more general discrete Gronwall-Bellman type inequalities in three independent variables which might be useful tools in the analysis of certain classes of partial finite difference and sum-difference equations.
Without stability of finite difference approximation, it is difficult to observe convergence property on the standard double precision arithmetic environments of computers, but it is possible to do it on a multiple-precision environment (e.g.
[18] consists in applying first trapezoidal integration to (2) and then using the following finite difference approximations:
Corless, "Compact finite difference method for integro-differential equations," Applied Mathematics and Computation, vol.
We establish the three layers finite difference schemes based on the problem of (1)-(3), as follows:
Finite difference method replaces the main differential equation with the system of algebraic equations that links shifts of observed points relative to neighbouring points.

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