Piecewise Legendre Spectral-collocation Method For A Class Of Singularly Perturbed Equations

This paper will study the piecewise Legendre spectral collocation method for a class of singularly perturbed equations to enrich the numerical solution methods for such problems in practical applications,the specific contents are as follows:Chspter Ⅰ is the introduction,which introduces the research background and current research progress of singularly perturbed Volterra integral problem and singularly perturbed Volterra integro-differential problem,as well as the main work of this dissertation.In Chspter Ⅱ,It provides the basic definition,related theory and grid construction required by the paper,we makes preparation for the following configuration method to solve the equation and stability analysis.In Chspter Ⅲ,the piecewise Legendre spectral collocation method of singular perturbated Volterra integrals is studied.The Legendre spectral allocation method is used on Shishkin grids and Vulanovi(?)-Bakhvaolv grids.The convergence analysis shows that the error decays exponentially.Numerical experiments verify the theoretical results given in this chapter.In Chspter Ⅳ,the piecewise Legendre spectral collocation method is constructed for the singularly perturbed Volterra integro-differential problem,the corresponding error estimates are derived.Two examples are given to verify the theoretical results in this chapter.Numerical experimental results show that piecewise Legendre spectral allocation method is very effective.