Sinc Method For Fourth-order Partial Integro-differential Equations

On practical problems in engineering and physics,often can encounter such as memory material heat conduction,move Mechanics,atomic reactions,etc.These problems usually involve parabolic partial integro-differential equations,for numerical solutions of such equations.Domestic Chen Chuanmiao,Xu Da et al.,foreign Ch.Lubich,V.thomee,W.Mclean,L.Wahlbin[25],Sanz-Serna[24] et al.have done a lot of research,they used spline configuration method,finite element method and spectrum configuration method,but few involved sinc discrete method.sinc collocation method uses sinc functions(Stenger 1981[3],Lund and Bowers 1992[8],Stenger 1993[21])as a basis function to construct the differential quadrantal method,and on this basis to solve the differential equation.The sinc function is used to study the approximate morphology in the analytic function space.After the exponential transformation of the approximation method of sinc function,the error of the approximation to the true solution can reach exponential convergence.Therefore,when solving the differential equation,the sinc collocation method can achieve high efficiency and high precision,so there's great significance for the calculation method of the numerical solution of the differential equation.This paper discusses the sinc discrete method for the fourth-order partial integrodifferential equation,and the boundary value problem of this kind of equation is solved by sinc discrete method.It is proved that the discrete solutions converge exponentially to the true solutions of partial integro-differential equations.In this paper,Euler method is used in time direction,and sinc method is used in space direction.Several numerical examples are given to illustrate the reliability and effectiveness of the sinc method.