High-Order Combined Compact Difference Schemes For Non-Self-Adjoint And Nonlinear Schrodinger Equation

In this thesis,we mainly propose some efficient numerical schemes for non-self-adjoint and nonlin-ear Schrodinger equation.LP-HOCCDI scheme and LP-HOCCD ? scheme scheme are constructed for it which we used the three-point sixth-order high order combined compact difference(HOCCD)scheme for spatial discretization and second-order leap-frog(LF)scheme for time discretization to construct high precision numerical schemes.In order to improve the stability,the LF-HOCCD? scheme is discretized in time direction by Crank-Nicolson(CN)scheme to construct the CN-HOCCD? scheme.Since this scheme needs to solve the nonlinear terms,and in order to improve the computational efficiency,the semi explicit?CN-HOCCD ? scheme which adopt extrapolation method to process the nonlinear terms is constructed.In Chapter 1,we first introduce the background,the research status at home and abroad and the prac-tical significance of non-self-adjoint and nonlinear Schrodinger equation.Then the preliminary knowledge used in this thesis is introduced.Last,the development and basic constructive ideas of the high-order compact(HOC)scheme are discussed.In Chapter 2,the basic ideas and constructive theories of HOCCD scheme are described.Then LP-HOCCD ? scheme,LP-HOCCD ? scheme,CN-HOCCD ? scheme and CN-HOCCD II scheme are proposed,and the calculation ideas of the new schemes are studied respectively.In Chapter 3,using numerical experiments,the validity and reliability of the proposed schemes are tested,and the advantages and disadvantages between the schemes are obtained by comparison.In Chapter 4,a summary of the work we have done in this thesis is given,accompanied with the en-visaged and prospects for the future study,including stability and convergence analysis,HOCCD scheme applied to other equations etc.