Compact implicit integration factor method for a class of high order differential equations
主 题: Compact implicit integration factor method for a class of high order differential equations
报告人: Prof. Xinfeng Liu（Department of Mathematics, University of South Carolina）
时 间: 2014-05-19 16:00-17:00
地 点: BICMR 全斋29（主持人：张磊）
When developing efficient numerical methods for solving parabolic types of equations, severe temporal stability constraints on the time step are often required due to the high-order spatial derivatives and/or stiff reactions. The implicit integration factor (IIF) method, which treats spatial derivative terms explicitly and reaction terms implicitly, can provide excellent stability properties in time with nice accuracy. One major challenge for the IIF is the storage and calculation of the dense exponentials of the sparse discretization matrices resulted from the linear differential operators. The compact representation of the IIF (cIIF) can overcome this shortcoming and greatly save computational cost and storage. In this talk, by treating the discretization matrices in diagonalized forms, we will present an efficient cIIF method for solving a family of semilinear fourth-order parabolic equations, in which the bi-Laplace operator is explicitly handled and the computational cost and storage remain the same as to the classic cIIF for second-order problems. In particular, the proposed method can deal with not only stiff nonlinear reaction terms but also various types of homogeneous or inhomogeneous boundary conditions.