This paper reprents two types of fully discrete Galerkin algorithm and nonlinear Galerkin algoritlun with variable time steps for solving numerically nonlinear evolution equations, in which spatial discretization is m...This paper reprents two types of fully discrete Galerkin algorithm and nonlinear Galerkin algoritlun with variable time steps for solving numerically nonlinear evolution equations, in which spatial discretization is made by spectral functions and finite elements; time is done by the Euler explicit difference scheme with the first order accuracy and two-step semi-implicit difference scheme with the second order accuracy. According to the stability analysis, we find that for the Euler difference scheme and two-step difference scheme on time discretization the stability of the fully discrete nonlinear Galerkin algorithms is superior to ones of the fully discrete Galerkin a-lgorithms. Finally, our numerical test also shows this fact.展开更多
In this paper, three general principles for constructing approximate inertial manifolds are provided, under which the associate approximate inertial form of origin problem, which is a finite dimensional ordinary diffe...In this paper, three general principles for constructing approximate inertial manifolds are provided, under which the associate approximate inertial form of origin problem, which is a finite dimensional ordinary differential equation, is well-possed and its solution will approximate the genuine solution at some degree. At last, for some kinds of approximate inertial manifolds and a family of approximate inertial manifolds, we indicate that the principles given here are suitable.展开更多
文摘This paper reprents two types of fully discrete Galerkin algorithm and nonlinear Galerkin algoritlun with variable time steps for solving numerically nonlinear evolution equations, in which spatial discretization is made by spectral functions and finite elements; time is done by the Euler explicit difference scheme with the first order accuracy and two-step semi-implicit difference scheme with the second order accuracy. According to the stability analysis, we find that for the Euler difference scheme and two-step difference scheme on time discretization the stability of the fully discrete nonlinear Galerkin algorithms is superior to ones of the fully discrete Galerkin a-lgorithms. Finally, our numerical test also shows this fact.
基金The National Natural Science Foundation of China(1117126911401174)+8 种基金the Ph.D.Programs Foundation of Ministry of Education of China(20110201110027)the China Postdoctoral Science Foundation(2013M531311)the Henan Scientific and Technological Research Project(132102310309)the Educational Commission of Henan Province of China(14B11002014B11002114B110025)the Doctoral Foundation of Henan University of Science and Technology(09001625)the Science Foundation for Cultivating Innovation Ability of Henan University of Science and Technology(2014ZCX009)the Youth Scientific Foundation of Henan University of Science and Technology(2012QN029)
文摘In this paper, three general principles for constructing approximate inertial manifolds are provided, under which the associate approximate inertial form of origin problem, which is a finite dimensional ordinary differential equation, is well-possed and its solution will approximate the genuine solution at some degree. At last, for some kinds of approximate inertial manifolds and a family of approximate inertial manifolds, we indicate that the principles given here are suitable.
