Numerical analysis and computational solution of integro-differential equations

报告题目: Numerical analysis and computational solution of integro-differential equations


报告人: Hermann Brunner

Department of Mathematics Hong Kong Baptist University

and Department of Mathematics and Statistics Memorial University of  Newfoundland




地点: 理科楼数学系A404


摘要:Volterra first studied (partial) integro-differential equations in his papers of 1909 and 1912, and he observed that in order to solve such problems''it is necessary to employ an analysis that is rather different from the one used for differential or integral equations''. This observation applies equally well to the numerical analysis and the computational solution of ordinary and partial Volterra integro-differential equations (VIDEs), not least because in the mathematical modelling of hereditary phenomena these equations often occur in non-classical forms.


I will describe typical examples of such integro-differential equations in the first part of my talk. This will be followed by a brief review of theoretical aspects of important classes of time-stepping schemes (collocation methods; discontinuous Galerkin methods and their $hp$-versions; methods based on convolution quadrature) for ordinary and partial VIDEs. In the last part of the talk I shall describe some recent approaches to the computational solution of certain non-standard integro-differential equations (including nonlinear ones of Fredholm type) and show that many challenging problems remain to be addressed.


报告人简介:Hermman Brunner 教授是积分-微分方程领域的著名专家,在积分-微分方程的理论和数值解的研究方面做出了很多开创性的工作。是SIAM Journal on Numerical AnalysisIMA Journal of Numerical AnalysisJournal of Integral Equations and Applications等学术期刊的编委。是Atlantic Association for Research in the Mathematical Sciences的前主席(2009-2013). 获得过 2008 David Borwein Distinguished Career Award (Canadian Mathematical Society) Fellow of the Fields Institute.




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