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 , 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
The computed solutions can then be refined by the finite element method or the finite difference
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.
 consists in applying first trapezoidal integration to (2) and then using the following finite difference
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:
method replaces the main differential equation with the system of algebraic equations that links shifts of observed points relative to neighbouring points.