Skip to main content

variational method

variational method A technique for the solution of certain classes of ordinary and partial differential equations that involves the use of a variational principle. That is, the solution of the differential equation is expressed as the solution of a minimization problem that involves an integral expression. The equation is then solved by carrying out an approximate minimization. Variational principles arise naturally in many branches of physics and engineering. As an example, the solution of y + q(x)y = f(x), 0←x←1 y(0) = y(1) = 0

is also the solution of the problem

where V is a class of sufficiently differentiable functions that are zero at x = 0 and x = 1. An approximate minimization can be carried out by minimizing over the subspace of functions

When the trial functions φj(x) are splines, the resulting method is an example of the finite-element method.

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"variational method." A Dictionary of Computing. . 19 Mar. 2019 <>.

"variational method." A Dictionary of Computing. . (March 19, 2019).

"variational method." A Dictionary of Computing. . Retrieved March 19, 2019 from

Learn more about citation styles

Citation styles 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, cannot guarantee each citation it generates. Therefore, it’s best to use 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 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.