TY - JOUR
T1 - Efficient methods for Volterra integral equations with highly oscillatory Bessel kernels
AU - Xiang, Shuhuang
AU - Brunner, Hermann
N1 - Funding Information:
This work is supported partly by NSF of China (No.11071260).
PY - 2013/3
Y1 - 2013/3
N2 - In this paper, we introduce efficient methods for the approximation of solutions to weakly singular Volterra integral equations of the second kind with highly oscillatory Bessel kernels. Based on the asymptotic analysis of the solution, we derive corresponding convergence rates in terms of the frequency for the Filon method, and for piecewise constant and linear collocation methods. We also present asymptotic schemes for large values of the frequency. These schemes possess the property that the numerical solutions become more accurate as the frequency increases.
AB - In this paper, we introduce efficient methods for the approximation of solutions to weakly singular Volterra integral equations of the second kind with highly oscillatory Bessel kernels. Based on the asymptotic analysis of the solution, we derive corresponding convergence rates in terms of the frequency for the Filon method, and for piecewise constant and linear collocation methods. We also present asymptotic schemes for large values of the frequency. These schemes possess the property that the numerical solutions become more accurate as the frequency increases.
KW - Bessel function kernel
KW - Highly oscillatory kernel
KW - Volterra integral equation
KW - Weak kernel singularity
UR - http://www.scopus.com/inward/record.url?scp=84874807053&partnerID=8YFLogxK
U2 - 10.1007/s10543-012-0399-8
DO - 10.1007/s10543-012-0399-8
M3 - Journal article
AN - SCOPUS:84874807053
SN - 0006-3835
VL - 53
SP - 241
EP - 263
JO - BIT Numerical Mathematics
JF - BIT Numerical Mathematics
IS - 1
ER -