Stability of VDRK methods for linear Volterra integro-differential equations

主讲人：黄乘明华中科技大学教授

时间：2019年10月19日14：30

地点：10号楼247室

举办单位：数理学院

内容介绍：In theory, stiffly accurate schemes like the implicit Euler scheme apply for semi-explicit index-2 DAEs without order reduction. If, however, during the time stepping, the resulting algebraic systems are solved not exactly, this error is amplified by the inverse of the time step. We use the discrete Kronecker index to analyse this source of instability. This analysis also includes time stepping schemes that cannot be interpreted as a time-discrete version of a continuous time DAE. For the application example of the incompressible Navier-Stokes equations, we show that the SIMPLE and the projection schemes that are commonly used in practice, factually reduce the discrete Kronecker index.