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