Monotone Numerical Methods for Nonlinear Parabolic Problems
主 题: Monotone Numerical Methods for Nonlinear Parabolic Problems
报告人: Igor Boglaev (Massey University)
时 间: 2016-08-10 16:00-17:00
地 点: 数学中心 全斋9教室(数学中心计算方法与应用实验室活动,北京计算数学学会系列报告)
The talk is concerned with monotone numerical methods for nonlinear
parabolic problems. Various monotone iterative methods, including the monotone
fully implicit, the monotone weighted average and the monotone ADI methods, are
presented. The basic idea of the iterative methods for the computation of
numerical solutions is the monotone approach which involves the notion of upper
and lower solutions and the construction of monotone sequences from a suitable
linear discrete system. Using upper and lower solutions as two distinct initial
iterations, two monotone sequences from a suitable linear system are constructed.
The monotone property of the iterations gives improved upper and lower bounds
of the solution in each iteration. Error estimates between the computed
approximations and the solutions of the nonlinear discrete problems are
obtained for each monotone iterative method. The monotone convergence property
is used to prove the convergence of the nonlinear discrete problems to the
corresponding differential problems as mesh sizes decrease to zero.
Applications are given to several models arising from physical, chemical and
biological systems. Numerical experiments are given to some of these models,
including a discussion on a rate of convergence of the monotone sequences.
