Engineers in various fields explore techniques that reduce or eliminate the type of meshes required by first-generation computational methods, such as

finite differences or finite elements.

Algorithms of

Finite Differences, Moment method, Finite Element method and

Finite Difference Time Domain method are each informatively illustrated in the pages of "Advanced Electromagnetic Computation".

The techniques being used here come from a branch of mathematics known as

finite differences. The tables in Kok's article showing the incremental changes in the y-values can be called difference tables.

For the first form of the

finite difference filter, we apply the central

finite differences to obtain a discretization of the nonlinear fourth-order boundary value problem.

An introductory section provides the method of weighted residuals development of

finite differences, finite volume, finite element, boundary element, and meshless methods along with 1-D examples of each method.

Many researchers who have worked on equation (1) i.e.(Collatz1973; Crandall1954; Conte and Royster1956; Conte1957; Evans1965; Jain et al.1976;Richtmyerand Mortan 1967) by using

finite differences and reducing equation (1) in a system of second orderpartial differential equations.

Finite differences and singularities in elliptic problems" in: A Survey of Numerical Methods for Partial Differential Equations I.

Laplace's equation in

finite differences is of the following form

The approximation of derivatives by

finite differences is the cornerstone of numerical computing.

Instead of using spectral method, the CFDRM uses the compact

finite differences to integrate the linearized system of differential equations.

Pratt, "Frequency-domain elastic wave modeling by

finite differences: a tool for crosshole seismic imaging," Geophysics, vol.