Premium
Weakly Singular Discrete Gronwall Inequalities
Author(s) -
Dixon J.,
McKee S.
Publication year - 1986
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19860661107
Subject(s) - discretization , mathematics , gronwall's inequality , convergence (economics) , kernel (algebra) , mathematical analysis , work (physics) , integral equation , inequality , pure mathematics , mechanical engineering , engineering , economics , economic growth
Abstract Generalizations of the classical Gronwall inequality when the kernel of the associated integral equation is weakly singular are presented. The continuous and discrete versions are both given; the former is included since it suggests the latter by analogy. This work is motivated by convergence studies of discretization methods for Volterra integral and integro‐differential equations. The results are all given in a form designed to be of most use to numerical analysts.