Compact Finite Volume Methods For The Multi-term Time Fractional Sub-diffusion Equations

In this paper,a compact finite volume method is proposed for the multi-term time fractional sub-diffusion equation.This method is based on the idea of com-pact difference method.This method discretizes spatial derivative by using finite volume method,and then discretizes eime fractional derivative by using classical1interpolation.The scheme has good integral conservation.This paper is divided into four chapters.The first chapter is the introduction,and it introduces the physical background of the multi-term time fractional sub-diffusion equation and the development of the compact finite volume method,and research status of such equations.In chapter two,a compact finite volume scheme is proposed for the one-dimensional multi-term time fractional sub-diffusion equation.The linear algebraic equations formed by this scheme are easy to solve.Finally,it is proved that the scheme has fourth order accuracy in spatial direction and 2-order accuracy in temporal direction according to discrete~?norm.Numerical examples also verify the correctness of the theoretical analysis and the validity of the format.In chapter three,according to the similar idea as chapter two,a compact finite volume scheme is proposed for the two-dimensional multi-term time fractional sub-diffusion equation.Similarly,the equations formed by this scheme have tridiagonal property.The last numerical example also shows that the discrete~?norm have fourth-order accuracy in spatial direction and 2-order accuracy in temporal direction.Chapter two and chapter three show that the compact finite volume scheme proposed in this paper has high accuracy and stability.Chapter four is a summary of the whole paper and a prospect of the future work.