Numerical analysis and computational solution of integro-differential equations

TitleNumerical analysis and computational solution of integro-differential equations

 

Speaker Hermann Brunner

Department of Mathematics Hong Kong Baptist University

and Department of Mathematics and Statistics Memorial University of  Newfoundland

 

Date:  16:00-17:00 pm, July 16, 2014

 

Place: Conference Room A404, Department of Mathematical Sciences

 

AbstractVolterra 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.

 

ContactDongSheng Yin