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In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with any other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. [ 1 ]
Ordinary differential equations occur in many scientific disciplines, including physics, chemistry, biology, and economics. [1] In addition, some methods in numerical partial differential equations convert the partial differential equation into an ordinary differential equation, which must then be solved.
It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler , who first proposed it in his book Institutionum calculi integralis (published 1768–1770).
The Bogacki–Shampine method is a method for the numerical solution of ordinary differential equations, that was proposed by Przemysław Bogacki and Lawrence F. Shampine in 1989 (Bogacki & Shampine 1989).
The backward differentiation formula (BDF) is a family of implicit methods for the numerical integration of ordinary differential equations.They are linear multistep methods that, for a given function and time, approximate the derivative of that function using information from already computed time points, thereby increasing the accuracy of the approximation.
The corresponding ordinary differential operator is the radial part of the Laplacian operator on 2-dimensional hyperbolic space. More generally, the Plancherel theorem for SL(2,R) of Harish Chandra and Gelfand – Naimark can be deduced from Weyl's theory for the hypergeometric equation, as can the theory of spherical functions for the isometry ...
This is a list of named linear ordinary differential equations. A–Z. Name Order Equation Applications Airy: 2 = [1] ...
Pages in category "Ordinary differential equations" The following 141 pages are in this category, out of 141 total. ... Liouville's formula; Lommel function;