Numerical Solution Of Fourth-order Time-fractional Parabolic Equations Based On Sinc-collocation

Fractional calculus is a branch of calculus,which is used to study signal processing,system recognition,optical system,thermal system and other ap-plication field problems because of its memory and hereditary properties.Such problems have received more and more attention and research from scholars at home and abroad.In this paper,we study the numerical method for solving fourth-order time fractional partial differential equations.In the proposed method,Euler method is used to discretize the time derivative to get the semi-discrete scheme and the Sine collocation method is applied to approximate the spatial derivative to obtain the fully discrete scheme.Then the error analysis of the full discrete scheme is carried out,and the stability and convergence of the scheme are obtained.The convergence order reaches exponential convergence in spatial direction.Finally,some numerical example are given to verify our conclusion.The main contents of this paper are arranged as follows:The first chapter introduces the research background and current status of partial differential equations at home and abroad.Chapter 2 describes some basic knowledge of the Sine collocation method and fractional calculus.Chapter 3 gives the fully discrete scheme and the convergence analysis.In Chapter 4,some numerical examples are used to verify that the Sine collcation method can effectively solve the fourth-order time fractional partial differential equations.