Adaptive, Fast, and Oblivious Convolution in Evolution Equations with Memory
نویسندگان
چکیده
منابع مشابه
Adaptive, Fast, and Oblivious Convolution in Evolution Equations with Memory
To approximate convolutions which occur in evolution equations with memory terms, a variable-stepsize algorithm is presented for which advancing N steps requires only O(N log N) operations and O(log N) active memory, in place of O(N) operations and O(N) memory for a direct implementation. A basic feature of the fast algorithm is the reduction, via contour integral representations, to differenti...
متن کاملFast and Oblivious Convolution Quadrature
We give an algorithm to compute N steps of a convolution quadrature approximation to a continuous temporal convolution using only O(N logN) multiplications and O(logN) active memory. The method does not require evaluations of the convolution kernel, but instead O(logN) evaluations of its Laplace transform, which is assumed sectorial. The algorithm can be used for the stable numerical solution w...
متن کاملQCDNUM: Fast QCD evolution and convolution
The qcdnum program numerically solves the evolution equations for parton densities and fragmentation functions in perturbative QCD. Un-polarised parton densities can be evolved up to next-to-next-to-leading order in powers of the strong coupling constant, while polarised densities or fragmentation functions can be evolved up to next-to-leading order. Other types of evolution can be accessed by ...
متن کاملAdaptive Steffensen-like Methods with Memory for Solving Nonlinear Equations with the Highest Possible Efficiency Indices
The primary goal of this work is to introduce two adaptive Steffensen-like methods with memory of the highest efficiency indices. In the existing methods, to improve the convergence order applied to memory concept, the focus has only been on the current and previous iteration. However, it is possible to improve the accelerators. Therefore, we achieve superior convergence orders and obtain as hi...
متن کاملEfficient computing in evolution equations with memory
To approximate convolutions which occur in evolution equations with memory terms, a variable-step-size algorithm is presented for which advancing N steps requires only O(N logN) operations and O(logN) active memory, in place of O(N2) operations and O(N) memory for a direct implementation. A basic feature of the fast algorithm is the reduction, via contour integral representations, to differenti...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2008
ISSN: 1064-8275,1095-7197
DOI: 10.1137/060674168