Orthogonal Spline Collocation Methods For A Class Of Partial Integro-Differential Equations

The integro-differential equation of parabolic type often occurs in application such as heat conduction in material with memory,compression of poroviscoelastic media,population dynamics,nuclear reactor dynamics,etc..there are lots of documents of V.Thom(?)e,Ch.Lubich,L.Wahlbin,G.Fairweather in overseas and Chuanmiao Chen,Chuanju Xu,Tao Tang,Zhizhong Sun,Da Xu in home.A lot of them use FEM;finite difference methods;spectral collocation methods;spline collocation methods.But a few of them make global behavior of full discretization by orthogonal spline collocation methods.We study a partial integrol-differential equations of parabolic type,using orthogonal spline collocation methods derived stabilities and error estimated respectively.Main results as follows:(1) Given the stability,error estimate of time semi-discretization Eular methods for the equation;(2)Given the stability and error estimate of full dis-cretization for the based on the orthogonal spline methods for the equation.(3)Numerical experiment.