TY - JOUR
T1 - Collocation Methods for General Volterra Functional Integral Equations with Vanishing Delays
AU - Xie, Hehu
AU - Zhang, Ran
AU - Brunner, Hermann
N1 - Funding information:
LSEC and Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China (hhxie@lsec.cc.ac.cn). This author’s work was supported by the National Science Foundation of China (NSFC 10801062,11001259).
School of Mathematics, Jilin University, Changchun 130012, China (zhangran@jlu.edu.cn). This author’s work was supported by NSFC (10801062, 11071102), Forefront of Science and Interdisciplinary Innovation Projects, Jilin University, the 985 project of Jilin University.
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL A1C 5S7 Canada, and Department of Mathematics, Hong Kong Baptist University, Hong Kong, China (hbrunner@math.hkbu.edu.hk). This author’s work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC Discovery Grant 9406) and by the Hong Kong Research Grants Council (HKBU 200207).
Publisher copyright:
Copyright © 2011 Society for Industrial and Applied Mathematics
PY - 2011/12/1
Y1 - 2011/12/1
N2 - We analyze the existence, uniqueness, and regularity properties of solutions for general Volterra functional integral equations with the delay function θ(t) vanishing at the initial point of the given interval [0, T] (with θ(t) = qt, 0 > q > 1, representing an important special case). The focus of the paper is then on the the attainable order of convergence, and the question of possible superconvergence, for collocation solutions in certain piecewise polynomial spaces. Numerical experiments complement the theoretical convergence results.
AB - We analyze the existence, uniqueness, and regularity properties of solutions for general Volterra functional integral equations with the delay function θ(t) vanishing at the initial point of the given interval [0, T] (with θ(t) = qt, 0 > q > 1, representing an important special case). The focus of the paper is then on the the attainable order of convergence, and the question of possible superconvergence, for collocation solutions in certain piecewise polynomial spaces. Numerical experiments complement the theoretical convergence results.
KW - Collocation solutions
KW - Existence and regularity of solutions
KW - Optimal order of convergence
KW - Pantograph-type delays
KW - Vanishing delays
KW - Volterra functional integral equations
UR - http://www.scopus.com/inward/record.url?scp=84856519440&partnerID=8YFLogxK
U2 - 10.1137/100818595
DO - 10.1137/100818595
M3 - Article
AN - SCOPUS:84856519440
VL - 33
SP - 3303
EP - 3332
JO - SIAM Journal of Scientific Computing
JF - SIAM Journal of Scientific Computing
SN - 1064-8275
IS - 6
ER -