Nyström method

The Nyström method of discretizing an integral equation uses a quadrature rule; i.e. applying the quadrature rule

$\int_a^b h (x) \;\mathrm d x \approx \sum_{k=1}^n w_k h (x_k)$

to, for example, the inhomogeneous Fredholm equation of the second kind

$f (x) = \lambda u (x) - \int_a^b K (x, x') u (x') \;\mathrm d x'$,

results in

$f (x) \approx \lambda u (x) - \sum_{k=1}^n w_k K (x, x_k) u (x_k)$.

References

• E. J. Nyström, Über die praktische Auflösung von Integralgleichungen mit Anwendungen auf Randwertaufgaben, Acta Mathematica 54 pp. 185-204 (1930).
• L. M. Delves & J. Walsh (eds) 1974 Numerical Solution of Integral Equations, Clarendon, Oxford.
• H.-J. Reinhardt 1985 Analysis of Approximation Methods for Differential and Integral Equations, Springer, New York.

This applied mathematics-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Integral equations Numerical analysis Numerical integration (quadrature) Applied mathematics stubs Wikimedia Foundation. 2010. Игры ⚽ Нужен реферат? Lorrie Wilmot Manila Headline Look at other dictionaries: Nystrom — is a surname of Danish, Norwegian and Swedish origin. Alternative spelling include Nyström, Nystrøm or Nystroem and can refer to: Contents 1 Nystrom 2 Nyström 3 Nystrøm 4 …   Wikipedia List of numerical analysis topics — This is a list of numerical analysis topics, by Wikipedia page. Contents 1 General 2 Error 3 Elementary and special functions 4 Numerical linear algebra …   Wikipedia List of mathematics articles (N) — NOTOC N N body problem N category N category number N connected space N dimensional sequential move puzzles N dimensional space N huge cardinal N jet N Mahlo cardinal N monoid N player game N set N skeleton N sphere N! conjecture Nabla symbol… …   Wikipedia William H. Starbuck — Infobox Scientist name = William Starbuck image width = 150px caption = birth date = birth date|1934|9|20|mf=y birth place = Portland, Indiana residence = citizenship = nationality = ethnicity = field = Cognitive Psychologist Organizational… …   Wikipedia Dendrimer — Figure 1: Dendrimer and dendron Dendrimers are repetitively branched molecules. [1] [2] The name comes from the Greek word δένδρον (pronounced dendron), which translates to tree . Synonymous terms for dendrimer include arborols and casca …   Wikipedia Dietmar Wittmann — Dietmar H. Wittmann, M.D., Ph.D., FACS is an academic surgeon specializing in complex abdominal surgery. He was associated with the following medical schools: University of Hamburg, Germany, University of Düsseldorf, Germany, University of… …   Wikipedia Numerical ordinary differential equations — Illustration of numerical integration for the differential equation y = y,y(0) = 1. Blue: the Euler method, green: the midpoint method, red: the exact solution, y = et. The step size is h = 1.0 …   Wikipedia Swedish inventions — are novel ideas and machines that have been pioneered in Sweden. In the 18th century Sweden s scientific revolution took off. Previously, technical progress had mainly come from professionals who had immigrated from mainland Europe. In 1739, the… …   Wikipedia Positivism — • A system of philosophical and religious doctrines elaborated by Auguste Comte. Catholic Encyclopedia. Kevin Knight. 2006. Positivism     Positivism      …   Catholic encyclopedia Finnish Civil War — Tampere s civilian buildings destroyed in the civil war. Date …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”