Romberg integration

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1: 3.5 Quadrature

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§3.5(iii) Romberg Integration

►Further refinements are achieved by Romberg integration. …With the Romberg scheme successive terms $c_1{h}^2,c_2{h}^4,\mathrm{\dots }$, in (3.5.9) are eliminated, according to the formula … ►When $f\in C^{\mathrm{\infty }}$, the Romberg method affords a means of obtaining high accuracy in many cases with a relatively simple adaptive algorithm. … ►See Davis and Rabinowitz (1984, pp. 440–441) for modifications of the Romberg method when the function $f$ is singular. …

2: 19.13 Integrals of Elliptic Integrals

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§19.13(i) Integration with Respect to the Modulus

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§19.13(ii) Integration with Respect to the Amplitude

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3: Alexander A. Its

… ►Current research areas of Its are mathematical physics, special functions, and integrable systems. … ► Novokshënov), published by Springer in 1986, Algebro-geometric Approach to Nonlinear Integrable Problems (with E. …

4: Vadim B. Kuznetsov

… ►Kuznetsov published papers on special functions and orthogonal polynomials, the quantum scattering method, integrable discrete many-body systems, separation of variables, Bäcklund transformation techniques, and integrability in classical and quantum mechanics. …

5: 9.14 Incomplete Airy Functions

… ►Incomplete Airy functions are defined by the contour integral (9.5.4) when one of the integration limits is replaced by a variable real or complex parameter. …

6: Alexander I. Bobenko

… ►Bobenko’s books are Algebro-geometric Approach to Nonlinear Integrable Problems (with E. … Eitner), published by Springer in 2000, and Discrete Differential Geometry: Integrable Structure (with Y. …He is also coeditor of Discrete Integrable Geometry and Physics (with R. …

7: 32.16 Physical Applications

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Integrable Continuous Dynamical Systems

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8: 36.15 Methods of Computation

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§36.15(iii) Integration along Deformed Contour

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§36.15(iv) Integration along Finite Contour

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9: Simon Ruijsenaars

… ►His main research interests cover integrable systems, special functions, analytic difference equations, classical and quantum mechanics, and the relations between these areas. …

10: Funding

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Systems Integration for Manufacturing Applications Program of the Engineering Laboratory (formerly Manufacturing Engineering Laboratory)

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