Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Composite Formulas Analysis

In course

MATH-251(c): Numerical analysis

Le cours présente des méthodes numériques pour la résolution de problèmes mathématiques comme des systèmes d'équations linéaires ou non linéaires, l'approximation de fonctions, l'intégration et la dérivation, et les équations différentielles. ...

Description

This lecture covers the analysis of composite formulas for numerical integration, focusing on the Simpson, trapezoid, and midpoint methods. It discusses the order of convergence, stability, and error analysis for each method, emphasizing the importance of accuracy and efficiency in numerical computations.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Instructors (2)

Fabio Nobile

Simone Deparis

Official source

Ontological neighbourhood

Mathematics

Analysis: Numerical analysis

Related concepts (32)

Trapezoidal rule

In calculus, the trapezoidal rule (also known as the trapezoid rule or trapezium rule; see Trapezoid for more information on terminology) is a technique for approximating the definite integral. The trapezoidal rule works by approximating the region under the graph of the function as a trapezoid and calculating its area. It follows that The trapezoidal rule may be viewed as the result obtained by averaging the left and right Riemann sums, and is sometimes defined this way.

Runge–Kutta methods

In numerical analysis, the Runge–Kutta methods (ˈrʊŋəˈkʊtɑː ) are a family of implicit and explicit iterative methods, which include the Euler method, used in temporal discretization for the approximate solutions of simultaneous nonlinear equations. These methods were developed around 1900 by the German mathematicians Carl Runge and Wilhelm Kutta. The most widely known member of the Runge–Kutta family is generally referred to as "RK4", the "classic Runge–Kutta method" or simply as "the Runge–Kutta method".

Simpson's rule

In numerical integration, Simpson's rules are several approximations for definite integrals, named after Thomas Simpson (1710–1761). The most basic of these rules, called Simpson's 1/3 rule, or just Simpson's rule, reads In German and some other languages, it is named after Johannes Kepler, who derived it in 1615 after seeing it used for wine barrels (barrel rule, Keplersche Fassregel). The approximate equality in the rule becomes exact if f is a polynomial up to and including 3rd degree.

Numerical integration

In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.

Riemann sum

In mathematics, a Riemann sum is a certain kind of approximation of an integral by a finite sum. It is named after nineteenth century German mathematician Bernhard Riemann. One very common application is approximating the area of functions or lines on a graph, but also the length of curves and other approximations. The sum is calculated by partitioning the region into shapes (rectangles, trapezoids, parabolas, or cubics) that together form a region that is similar to the region being measured, then calculating the area for each of these shapes, and finally adding all of these small areas together.

Related lectures (41)

Numerics: semester project

Covers the semester project on numerics, focusing on adaptive algorithms and multistep methods.

Numerical Integration: Newton-Cotes and Trapezoidal Rule

Covers numerical integration methods, including Newton-Cotes and the Trapezoidal Rule.

Explicit Stabilised Methods: Stochastic Differential Equations

Covers explicit stabilized methods for stiff stochastic differential equations, analyzing their properties and applications.

Numerical Integration: Lagrange Interpolation, Simpson Rules

Explains Lagrange interpolation for numerical integration and introduces Simpson's rules.

Numerical integration: continued Log in to Mediaspace to watch this video