Reduced Difference Algorithm Based On POD Method For Two Kinds Of Nonlinear Equations

In this thesis, the one-dimensional nonlinear Schr(o|¨ )dinger equation and the Symmetric Regularized Long Wave equation are studied. Firstly, the article introduces the physical background, using and numerical methods of these two equations. At the same time it presents the phylogeny, application and brief calculation processes of the POD method.Secondly, it introduces the use of Proper Orthogonal Decomposition method for solv-ing the one-dimensional nonlinear Schr(o|¨ )dinger equation and the Symmetric Regularized Long Wave equation. On the basis of the fourth order compact finite dierence scheme for the nonlinear Schr(o|¨ )dinger equation and the second order finite dierence scheme for the Symmetric Regularized Long Wave equation, reduced-order dierential algorithms are constructed. The error analysis proves the feasibility and convergence of reduced-order difference algorithm.Finally, numerical examples illustrate the reduced-order differential algorithms out-perform several other numerical formats on computational complexity and the computa-tion time with the same accuracy.