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Everything about Numerical integration
Methods of calculating definite integrals
In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral. The term numerical quadrature is more or less a synonym for "numerical integration", especially as applied to one-dimensional integrals. Some authors refer to numerical integration over more than one dimension as cubature; others take "quadrature" to include higher-dimensional integration. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Numerical integrationA 5-minute orientation
- Skim a recent paper: Understanding step selection analysis through numerical integrationInfluential work since 2022
- Pick up a classic book: Handbook of computational methods for integrationThe most-reprinted book on the subject
- Read the landmark paper: Numerical integration of the cartesian equations of motion of a system with constraints: molecular dynamics of n-alkanesCited 20,359 times
- Go sideways: IntegralA closely related topic
- Go sideways: Simpson's ruleA closely related topic
đź“– Definitions
Noun The study of numerical analysis algorithms to obtain approximate values of definite integrals.
🏆 Landmark papers (most cited)
Numerical integration of the cartesian equations of motion of a system with constraints: molecular dynamics of n-alkanes
Geometric Numerical Integration
Numerical Integration Over Simplexes
Construction of fully symmetric numerical integration formulas of fully symmetric numerical integration formulas
Numerical integration
Numerical integration on a triangle
Formulae for Numerical Integration
Extrapolation methods in numerical integration
🆕 Influential since 2022
Understanding step selection analysis through numerical integration
Tensor Neural Network and Its Numerical Integration
Small-Signal Stability Analysis of Numerical Integration Methods
Numerical Integration of locally Peaked Bivariate Functions
Quadratized Taylor series methods for ODE numerical integration
đź“š Books worth reading
Handbook of computational methods for integrationPrem K. Kythe, Michael R. Schaferkotter · 2004
Methods of numerical integrationPhilip J. Davis, Philip Rabinowitz · 1975- 📕A Three-dimensional Navier-Stokes/Euler code for blunt-body flow computationsChien-peng Li · 1985
Hypersingular integral equations and their applicationsI. K. Lifanov · 2003
Linear Integral EquationsRainer Kress · 1989
IntégrationNicolas Bourbaki · 1952
Advanced differential quadrature methodsZhi Zong · 2009- 📕Concise Introduction to Geometric Numerical IntegrationSergio Blanes, Fernando Casas · 2016
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đź”— Related topics
- Integral In mathematics, an integral is the continuous analog of a sum, and is used to calculate areas, volumes, and their generalizations. The process of computing…
- 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…
- Newton–Cotes formulas In numerical analysis, the Newton–Cotes formulas, also called the Newton–Cotes quadrature rules or simply Newton–Cotes rules, are a group of formulas for…
- 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…
- Gauss–Kronrod quadrature formula The Gauss–Kronrod quadrature formula is an adaptive method for numerical integration. It is a variant of Gaussian quadrature, in which the evaluation points…
- Clenshaw–Curtis quadrature Clenshaw–Curtis quadrature and Fejér quadrature are methods for numerical integration, or "quadrature", that are based on an expansion of the integrand…
- Trapezoidal rule In calculus, the trapezoidal rule (informally trapezoid rule; or in British English trapezium rule) is a technique for numerical integration, i.e. approximating…
- Gaussian quadrature In numerical analysis, an n-point Gaussian quadrature rule, named after Carl Friedrich Gauss, is a quadrature rule constructed to yield an exact result…