Perfectly Matched Layer Method For Nonlinear Wave Equations In Unbounded Domain

This paper focuses on the perfectly matched layer（PML）method of the time fractional Schr（?）dinger equation and Burgers’equation in an unbounded domain,which arise in many fields of application,such as quantum,mechanics.The research contents are as follows:The first chapter mainly introduces the background,significance and research status of time fractional wave equations in bounded domain and unbounded do-main,respectively,and introduces the research status of the perfectly matched layer method.In the second chapter,the numerical solution of the time fractional Schr（?）dinger equation is introduced.Based on Laplace transform,the appropriate PML formula for the time fractional Schr（?）dinger equation is derived.Then we prove that the formula is stable in one dimensional space.The fully discrete scheme of the PML formula can be deduced by using the finite difference method.Finally,through numerical experiments,the validity of the PML method of the time fractional Schr（?）dinger equation is verified,and several factors affecting the error are ana-lyzed.According to the numerical results,the following conclusions can be drawn:（1）The performance of PML is greatly improved when the absorbing layer is en-larged;（2）It exists an optimal absorption parameter₀;（3）An optimal wave number6)exists,such that the error is minimal.In chapter three,we apply the PML method to the time fractional Burger-s’equation.Similar to the time fractional Schr（?）dinger equation,we deduce the appropriate PML formula of the time fractional Burgers’equation and obtain the reduced initial boundary value problem on bounded domain.Finally,numerical examples show that this method is effective for time fractional Burgers’equation.Chapter four summarizes the content of this paper and looks forward to the future work.