where b, c, d, α, and β are given constants, the interval [0,1] is first divided into equal subintervals of length h; h is called the stepsize (or mesh or grid size). This gives the mesh points (or grid points) xn, xn = nh, n = 0,1,…,N+1, h = 1/(N+1)
At interior mesh points the derivatives are now replaced by finite-difference approximations, e.g. y′(xn) ≊ (½h)[y(xn+1) – y(xn–1)] y(xn) ≊ (1/h2)[y(xn+1) – 2y(xn) + y(xn–1)]
When combined with the boundary conditions these approximations result in a system of equations for approximations to y(xn), n = 1, 2,…, N. Nonlinear differential equations yield a system of nonlinear equations.
"finite-difference method." A Dictionary of Computing. . Encyclopedia.com. (April 21, 2019). https://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/finite-difference-method
"finite-difference method." A Dictionary of Computing. . Retrieved April 21, 2019 from Encyclopedia.com: https://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/finite-difference-method
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:
Modern Language Association
The Chicago Manual of Style
American Psychological Association
- Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
- In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.