Variable transformations in numerical integration
نویسندگان
چکیده
منابع مشابه
Numerical integration over smooth surfaces in R3 via class Sm variable transformations. Part I: Smooth integrands
Class Sm variable transformations with integer m for finite-range integrals were introduced by the author about a decade ago. These transformations ‘‘periodize’’ the integrand functions in a way that enables the trapezoidal rule to achieve very high accuracy, especially with even m. In a recent work by the author, these transformations were extended to arbitrary real m, and their role in improv...
متن کاملNumerical integration over smooth surfaces in R3 via class Sm variable transformations. Part II: Singular integrands
Class Sm variable transformations with integer m for finite-range integrals were introduced by the author about a decade ago. These transformations ‘‘periodize’’ the integrand functions in a way that enables the trapezoidal rule to achieve very high accuracy, especially with even m. In a recent work by the author, these transformations were extended to arbitrary real m, and their role in improv...
متن کاملA Novel Class of Symmetric and Nonsymmetric Periodizing Variable Transformations for Numerical Integration
Variable transformations for numerical integration have been used for improving the accuracy of the trapezoidal rule. Specifically, one first transforms the integral I [f ]= ∫ 1 0 f (x) dx via a variable transformation x = φ(t) that maps [0,1] to itself, and then approximates the resulting transformed integral I [f ] = ∫ 1 0 f ( φ(t) ) φ′(t) dt by the trapezoidal rule. In this work, we propose ...
متن کاملFurther extension of a class of periodizing variable transformations for numerical integration
Class Sm variable transformations with integer m, for accurate numerical computation of finite-range integrals via the trapezoidal rule, were introduced and studied by the author. A representative of this class is the sinm -transformation. In a recent work of the author, this class was extended to arbitrary noninteger values of m, and it was shown that exceptionally high accuracies are achieved...
متن کاملApplication of class Sm variable transformations to numerical integration over surfaces of spheres
ClassSm variable transformationswith integerm for finite-range integrals were introduced by the author (Numerical Integration IV, International series of Numerical Mathematics, Basel, 1993, pp. 359–373) about a decade ago. These transformations “periodize” the integrand functions in a way that enables the trapezoidal rule to achieve very high accuracy, especially with even m. In a recent work b...
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ژورنال
عنوان ژورنال: PAMM
سال: 2007
ISSN: 1617-7061,1617-7061
DOI: 10.1002/pamm.200700104