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Lady Windermere's Fan (mathematics)
In mathematics, Lady Windermere's Fan is a telescopic identity employed to relate global and local error of a numerical algorithm. The name is derived from Oscar Wilde's 1892 play '' Lady Windermere's Fan, A Play About a Good Woman''. Lady Windermere's Fan for a function of one variable Let E(\ \tau,t_0,y(t_0)\ ) be the exact solution operator so that: ::y(t_0+\tau) = E(\tau,t_0,y(t_0))\ y(t_0) with t_0 denoting the initial time and y(t) the function to be approximated with a given y(t_0). Further let y_n, n \in \N,\ n\le N be the numerical approximation at time t_n, t_0 < t_n \le T = t_N. can be attained by means of the approximation operator so that: :: with The approximation operator represents the numerical scheme used. For a simple explicit forward |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical models in science and engineering. Examples of numerical analysis include: ordinary differential equations as found in celestial mechanics (predicting the motions of planets, stars and galaxies), numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulating living cells in medicine an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oscar Wilde
Oscar Fingal O'Flahertie Wills Wilde (16 October 185430 November 1900) was an Irish poet and playwright. After writing in different forms throughout the 1880s, he became one of the most popular playwrights in London in the early 1890s. He is best remembered for his epigrams and plays, his novel '' The Picture of Dorian Gray'', and the circumstances of his criminal conviction for gross indecency for consensual homosexual acts in "one of the first celebrity trials", imprisonment, and early death from meningitis at age 46. Wilde's parents were Anglo-Irish intellectuals in Dublin. A young Wilde learned to speak fluent French and German. At university, Wilde read Greats; he demonstrated himself to be an exceptional classicist, first at Trinity College Dublin, then at Oxford. He became associated with the emerging philosophy of aestheticism, led by two of his tutors, Walter Pater and John Ruskin. After university, Wilde moved to London into fashionable cultural and social ci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lady Windermere's Fan
''Lady Windermere's Fan, A Play About a Good Woman'' is a four-act comedy by Oscar Wilde, first performed on Saturday, 20 February 1892, at the St James's Theatre in London. The story concerns Lady Windermere, who suspects that her husband is having an affair with another woman; she confronts him with it. Although he denies it, he invites the other woman, Mrs Erlynne, to his wife's birthday ball. Angered by her husband's supposed unfaithfulness, Lady Windermere decides to leave her husband for another lover. After discovering what has transpired, Mrs Erlynne follows Lady Windermere and attempts to persuade her to return to her husband and in the course of this, Mrs Erlynne is discovered in a compromising position. It is then revealed that Mrs Erlynne is Lady Windermere's mother, who abandoned her family twenty years before the time the play is set. Mrs Erlynne sacrifices herself and her reputation to save her daughter's marriage. Composition By the summer of 1891 Wilde had alr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler Method
In mathematics and computational science, the Euler method (also called forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. 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 treated it in his book '' Institutionum calculi integralis'' (published 1768–1870). The Euler method is a first-order method, which means that the local error (error per step) is proportional to the square of the step size, and the global error (error at a given time) is proportional to the step size. The Euler method often serves as the basis to construct more complex methods, e.g., predictor–corrector method. Informal geometrical description Consider the problem of calculating the shape of an unknown curve which starts at a given point and satisfies a given differential ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Error
In software engineering and mathematics, numerical error is the error in the numerical computations. Types It can be the combined effect of two kinds of error in a calculation. * the first is caused by the finite precision of computations involving floating-point or integer values * the second usually called truncation error is the difference between the exact mathematical solution and the approximate solution obtained when simplifications are made to the mathematical equations to make them more amenable to calculation. The term truncation comes from the fact that either these simplifications usually involve the truncation of an infinite series expansion so as to make the computation possible and practical, or because the least significant bits of an arithmetic operation are thrown away. Measure Floating-point numerical error is often measured in ULP (unit in the last place). See also * Loss of significance * Numerical analysis * Error analysis (mathematics) * Round-off error ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
