A Semi-implicit Finite Difference Scheme For The Multi-term Time-fractional Burgers-type Equations

In this dissertation,we construct a semi-implicit finite difference(FD)scheme for solving multi-term time-fractional Burgerstype equations,which will be completed in the following steps.Firstly,the L2-discretization formula is applied to the discretization of the multi-term Caputo fractional derivatives.Secondly,the second-order spatial derivative is approximated by using the second-order central difference quotient approximation and the nonlinear convection term uuxis discretized via the semi-implicit method.In this way,we have established a completely fully discrete scheme.In the theoretical analysis,we use the discrete energy method and the mathematical induction method to obtain the unconditional stability and convergence of the semi-implicit algorithm under the maximum norm.Finally,we verified the correctness and feasibility of the semi-implicit algorithm by analyzing the results of numerical experiments.The main content of this article is arranged as follows: In chapter 1,the research background and significance of fractional partial differential model are introduced,and the main content and present situation of the research are described in detail.In chapter 2,the basic definition and important lemmas of the semiimplicit algorithm are given,and the proof process of some lemmas is given.In Chapter 3,the semi-implicit FD scheme of mult-term time fractional Burgers type equation establishes the full discrete process.The stability and convergence analysis of the semi-implicit FD scheme are carried out in chapter 4.In chapter 5,that the results are consistent with the theoretical analysis is verified by the numerical examples.The summary of this article and some prospects for follow-up work in chapter 6.