Translation and analysis of words by ChatGPT artificial intelligence
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difference$21232$ - translation to greek
![stencil]] for the most common explicit method for the heat equation.](https://commons.wikimedia.org/wiki/Special:FilePath/Explicit method-stencil.svg?width=200 "stencil]] for the most common explicit method for the heat equation.")
![The control panel of the Time Zone Clock in front of [[Coventry Transport Museum]]](https://commons.wikimedia.org/wiki/Special:FilePath/Coventry Time Zone Clock.jpg?width=200 "The control panel of the Time Zone Clock in front of [[Coventry Transport Museum]]")
.png?width=200 "1913 time zone map of the United States, showing boundaries very different from today")
Definition
Wikipedia
In numerical analysis, finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences. Both the spatial domain and time interval (if applicable) are discretized, or broken into a finite number of steps, and the value of the solution at these discrete points is approximated by solving algebraic equations containing finite differences and values from nearby points.
Finite difference methods convert ordinary differential equations (ODE) or partial differential equations (PDE), which may be nonlinear, into a system of linear equations that can be solved by matrix algebra techniques. Modern computers can perform these linear algebra computations efficiently which, along with their relative ease of implementation, has led to the widespread use of FDM in modern numerical analysis. Today, FDM are one of the most common approaches to the numerical solution of PDE, along with finite element methods.
