Piecewise Continuous Configuration Of Volterra Integral Equations

This paper mainly deals with the existence and uniqueness, global convergence,global superconvergence and local superconvergence of the collocation method forVolterra integro-diferential equations with piecewise continuous arguments. Themathematical models of this kind of equations have a very wide application in biol-ogy, physics, control science and other felds of science. Therefore, studying of thiskind of problems is of important theoretical values and practical signifcance.In Chapter1, the background and research history of Volterra integro-diferentialequations with piecewise continuous arguments are introduced, and the developmentstatus of the stability of the analytic and numerical solutions of diferential equa-tions, and the study status of Volterra integro-diferential equations with piecewisecontinuous arguments are surveyed.In Chapter2, the existence and uniqueness of the analytic solution for Volterraintegro-diferential equations with piecewise continuous arguments are studied. Thecorresponding collocation formula is given, and the existence and uniqueness of thecollocation solution are proved.In Chapter3, the global convergence of the collocation method for Volterraintegro-diferential equations with piecewise continuous arguments is analyzed form arbitrary collocation parameters.In Chapter4, when m collocation parameters are subject to some orthogonalityconditions, the global superconvergence and local superconvergence of the colloca-tion method for Volterra integro-diferential equations with piecewise continuousarguments are discussed.In Chapter5, some corresponding numerical experiments are given to verify thecorrectness of the conclusions obtained in this paper.