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.