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.
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.