• Thumbnail for Trapezoidal rule
    _{a}^{b}f(x)\,dx.} The trapezoidal rule works by approximating the region under the graph of the function f ( x ) {\displaystyle f(x)} as a trapezoid and calculating...
    17 KB (3,267 words) - 19:19, 24 June 2025
  • Thumbnail for Tai's model
    rectangles and triangles rather than trapezoids. A follow-up letter by the authors of "Tai's Formula is the Trapezoidal Rule" pointed out that each contiguous...
    8 KB (837 words) - 06:52, 24 June 2025
  • Thumbnail for Trapezoid
    the graph of the function by a collection of trapezoids, so this method is called the trapezoidal rule. When any rectangle is viewed in perspective from...
    33 KB (4,075 words) - 14:45, 12 July 2025
  • Thumbnail for Riemann sum
    Riemann sum (redirect from Rectangle rule)
    the average of the left and right Riemann sums is the trapezoidal rule and gives a trapezoidal sum. It is one of the simplest of a very general way of...
    21 KB (3,414 words) - 15:07, 25 March 2025
  • scientific computing, the trapezoidal rule is a numerical method to solve ordinary differential equations derived from the trapezoidal rule for computing integrals...
    5 KB (758 words) - 15:40, 16 September 2024
  • Thumbnail for Simpson's rule
    achieve the same accuracy as trapezoidal rule. Composite Simpson's 3/8 rule is even less accurate. Integration by Simpson's 1/3 rule can be represented as a...
    25 KB (4,941 words) - 06:14, 17 June 2025
  • to the improved or modified Euler's method (that is, the explicit trapezoidal rule), or a similar two-stage Runge–Kutta method. It is named after Karl...
    8 KB (1,278 words) - 09:07, 29 April 2024
  • approximate solution at t = t1 = t0 + h. This method is known as the "trapezoidal rule" for differential equations. Indeed, this method can also be derived...
    6 KB (858 words) - 09:48, 15 April 2025
  • Thumbnail for Integral
    A better approach, the trapezoidal rule, replaces the rectangles used in a Riemann sum with trapezoids. The trapezoidal rule weights the first and last...
    69 KB (9,288 words) - 03:06, 30 June 2025
  • Thumbnail for Numerical integration
    means of compass and straightedge. The ancient Babylonians used the trapezoidal rule to integrate the motion of Jupiter along the ecliptic. For a quadrature...
    23 KB (3,263 words) - 19:28, 24 June 2025
  • be constructed from the Euler method (an explicit method) and the trapezoidal rule (an implicit method). Consider the differential equation y ′ = f (...
    5 KB (792 words) - 17:19, 28 November 2024
  • numerical solution of a linear Volterra equation of the second kind is the trapezoidal rule, which for equally-spaced subintervals Δ x {\displaystyle \Delta x}...
    8 KB (1,496 words) - 10:11, 4 June 2025
  • concentration is measured at certain discrete points in time and the trapezoidal rule is used to estimate AUC. In pharmacology, the area under the plot of...
    11 KB (1,288 words) - 08:18, 25 May 2025
  • Thumbnail for Gaussian quadrature
    numerical analysis, an n-point Gaussian quadrature rule, named after Carl Friedrich Gauss, is a quadrature rule constructed to yield an exact result for polynomials...
    42 KB (6,854 words) - 04:08, 15 June 2025
  • method is based on the trapezoidal rule, giving second-order convergence in time. For linear equations, the trapezoidal rule is equivalent to the implicit...
    21 KB (3,806 words) - 16:22, 21 March 2025
  • Thumbnail for Newton–Cotes formulas
    Newton–Cotes formulas, also called the Newton–Cotes quadrature rules or simply Newton–Cotes rules, are a group of formulas for numerical integration (also called...
    9 KB (1,167 words) - 19:14, 23 May 2025
  • Thumbnail for Pharmacokinetics
    with the trapezoidal rule (numerical integration) the most common method. Due to the dependence on the length of x in the trapezoidal rule, the area...
    41 KB (4,312 words) - 01:45, 6 July 2025
  • Thumbnail for Runge–Kutta methods
    listed above. Another example for an implicit Runge–Kutta method is the trapezoidal rule. Its Butcher tableau is: 0 0 0 1 1 2 1 2 1 2 1 2 1 0 {\displaystyle...
    45 KB (7,400 words) - 05:32, 7 July 2025
  • Thumbnail for PSIM Software
    electronic circuit. Developed by Powersim, PSIM uses nodal analysis and the trapezoidal rule integration as the basis of its simulation algorithm. PSIM provides...
    10 KB (937 words) - 03:24, 30 April 2025
  • 0), is equivalent to the trapezoidal rule with 2n + 1 points; the first extrapolation, R(n, 1), is equivalent to Simpson's rule with 2n + 1 points. The...
    13 KB (1,687 words) - 15:13, 25 May 2025
  • where the first two methods are the backward Euler method and the trapezoidal rule respectively: y n = y n − 1 + h f ( t n , y n ) , y n + 1 = y n + 1...
    23 KB (4,869 words) - 10:00, 15 April 2025
  • numerical quadrature. It explains the superior performance of the trapezoidal rule on smooth periodic functions and is used in certain extrapolation methods...
    19 KB (3,779 words) - 03:07, 20 April 2025
  • Contour integration Laplace's method Numerical integration Simpson's rule Trapezoidal rule Risch algorithm Improper integrals Gaussian integral Dirichlet integral...
    29 KB (6,052 words) - 11:04, 24 May 2025
  • Thumbnail for Monte Carlo integration
    mean-field particle methods. In numerical integration, methods such as the trapezoidal rule use a deterministic approach. Monte Carlo integration, on the other...
    18 KB (2,612 words) - 16:57, 11 March 2025
  • derived by deductive reasoning. Babylonians may have discovered the trapezoidal rule while doing astronomical observations of Jupiter. From the age of Greek...
    55 KB (6,755 words) - 21:18, 6 July 2025
  • &1\end{array}}} The Crank–Nicolson method corresponds to the implicit trapezoidal rule and is a second-order accurate and A-stable method. 0 0 0 1 1 / 2 1...
    29 KB (5,495 words) - 23:06, 19 June 2025
  • See also list of numerical analysis topics Rectangle method Trapezoidal rule Simpson's rule Newton–Cotes formulas Gaussian quadrature Table of common limits...
    4 KB (389 words) - 12:14, 10 February 2024
  • stiff equations. An example of a second-order A-stable method is the trapezoidal rule mentioned above, which can also be considered as a linear multistep...
    25 KB (3,802 words) - 15:30, 29 April 2025
  • T {\displaystyle T} is the numerical integration step size of the trapezoidal rule used in the bilinear transform derivation; or, in other words, the...
    15 KB (2,867 words) - 01:36, 2 July 2025
  • Thumbnail for Quasi-Monte Carlo method
    one-dimensional integration, quadrature methods such as the trapezoidal rule, Simpson's rule, or Newton–Cotes formulas are known to be efficient if the...
    12 KB (1,741 words) - 11:16, 6 April 2025