mwang_pay (09/21/82)
DEPARTMENT OF COMPUTER SCIENCE
UNIVERSITY OF WATERLOO
SEMINAR ACTIVITIES
NUMERICAL ANALYSIS SEMINAR - Wednesday, Sept. 29, 1982.
Prof. H. Brunner of Universite de Fribourg Suisse
will speak on "The Numerical Solution of Volterra
Integral and Integro-Differential Equations with
Weakly Singular Kernels."
TIME: 3:30 PM
ROOM: M&C 6091A (Please Note)
ABSTRACT
Volterra integral equations of the second kind with
weakly singular kernels of the form
k (t,s,y) = (t-s) sup {- alpha } cdot g(t,s,y)
(0 < alpha < 1 ) have solutions which, in general,
possess unbounded derivatives at the left endpoint of
the interval of integration (an analogous result
holds for Volterra integro-differential equations).
This implies that numerical methods based, for exam-
ple, on collocation in polynomial spline spaces can
no longer possess the high order of convergence
obtained when applying these methods to equations
with smooth solutions. In this talk we shall deal
with the construction and the implementation of
numerical methods for which one can again achieve an
arbitrarily high order, especially near the point of
September 21, 1982
- 2 -
singular behavior of the exact solutions.
September 21, 1982