The Compact Finite Difference Method Of Cattaneo Model

Compared with the traditional diffusion equation and heat conduction equa-tion.the Cattaneo model modifies the traditional Fick law and Fourier law in the derivation process,so that it has finite propagation speed.Therefore,it has very important physical significance.It is widely used extended irreversible thermo-dynamics.cosmological,heat pulse propagation.At the same time,the numerica l solution important theoretical and practical significance.which has attracted more and more scholars' attention and rescearch.In this dissertation,a compact finite difference scheme is proposed for Cattaneo model.Compact finite difference,method is a kind of finite difference method with high precision,high resolution and low requirements on grid nodes,it has attracted the attention of many scholars.This dissertation is divided into five chapters.The first chapter is the intro-duction,which introduces the physical bakground and research status of Cattaneo model and the main content and structure of the paper are also described.In chap-ter 2,a compact difference scheme is proposed for the one-dimensional Cattaneo model,stability and convergence are analyzed by energy method,and the validi-ty of the scheme is verified by numerical experiments,and the Cattaneo model is compared with the heat conduction equation and the effect of relaxation param-eters is tested.In chapter 3,a compact diference scheme is proposed for the two-dimensional Cattaneo model.also through the energy method for theoretical analysis.In the numerical experiment,the exact solution of the specific problem is obtained by using the separation of variables method,and the validity of the scheme is verified by comparison with the numerical solution.Finally,the relaxation pa-rameters are also tested.In chapter 4,a compact difference scheme is proposed for the one-dimensional fractional Cattaneo model the stability and convergence are analyzed by energy method,and the validity by numerical experiments,at the same time,the effect of ? is tested.The fifth chapter is a summary of the work of the full text and the future work prospects.