Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient high order algorithms for fractional integrals and fractional
  differential equations   We propose an efficient algorithm for the approximation of fractional
integrals by using Runge--Kutta based convolution quadrature. The algorithm is
based on a novel integral representation of the convolution weights and a
special quadrature for it. The resulting method is easy to implement, allows
for high order, relies on rigorous error estimates and its performance in terms
of memory and computational cost is among the best to date. Several numerical
results illustrate the method and we describe how to apply the new algorithm to
solve fractional diffusion equations. For a class of fractional diffusion
equations we give the error analysis of the full space-time discretization
obtained by coupling the FEM method in space with Runge--Kutta based
convolution quadrature in time.

23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg