trapezoidal rule
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Trapezoidal rule — This article is about the quadrature rule for approximating integrals. For the Explicit trapezoidal rule for solving initial value problems, see Heun s method. The function f(x) (in blue) is approximated by a linear function (in red). In… … Wikipedia
trapezoidal rule — noun : an approximate rule for determining the area under a curve * * * Math. a numerical method for evaluating the area between a curve and an axis by approximating the area with the areas of trapezoids … Useful english dictionary
trapezoidal rule — Math. a numerical method for evaluating the area between a curve and an axis by approximating the area with the areas of trapezoids. * * * … Universalium
Simpson's rule — can be derived by approximating the integrand f (x) (in blue) by the quadratic interpolant P (x) (in red). In numerical analysis, Simpson s rule is a method for numerical integration, the numerical approximation of definite integrals.… … Wikipedia
Trapezium rule — In mathematics, the trapezium rule (the British term) or trapezoidal rule (the American term) is a way to approximately calculate the definite integral: int {a}^{b} f(x),dx. The trapezium rule works by approximating the region under the graph of… … Wikipedia
Clenshaw–Curtis quadrature — and Fejér quadrature are methods for numerical integration, or quadrature , that are based on an expansion of the integrand in terms of Chebyshev polynomials. Equivalently, they employ a change of variables x = cos θ and use a discrete… … Wikipedia
Numerical integration — consists of finding numerical approximations for the value S In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also… … Wikipedia
Stiff equation — In mathematics, a stiff equation is a differential equation for which certain numerical methods for solving the equation are numerically unstable, unless the step size is taken to be extremely small. It has proven difficult to formulate a precise … Wikipedia
Riemann sum — In mathematics, a Riemann sum is a method for approximating the total area underneath a curve on a graph, otherwise known as an integral. It may also be used to define the integration operation. The sums are named after the German mathematician… … Wikipedia
Integral — This article is about the concept of integrals in calculus. For the set of numbers, see integer. For other uses, see Integral (disambiguation). A definite integral of a function can be represented as the signed area of the region bounded by its… … Wikipedia
Collocation method — In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations. The idea is to choose a finite dimensional space of candidate solutions… … Wikipedia
