The talk is concerned with monotone numerical methods for nonlinear parabolic problems. 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. The monotone property of the iterations gives improved upper and lower bounds of the solution in each iteration. 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.

Professor Igor Boglaev obtained his PhD in Mathematics at Moscow Institute of Physics and Technology, in 1976. In 1989, Professor Igor Boglaev obtained his DSc in Mathematics and Computer Science at Lomonosov Moscow State University. In 1989-1994, he was a head of Department of Applied Mathematics at Institute of Microelectronic Technology, Russian Academy of Sciences. In 1994 and 1995, he was a research fellow at, respectively, University of Toronto and University of Auckland. From 1996, he has been  a full Professor and Chair in Computational Mathematics at Massey University, New Zealand. Professor Igor Boglaev's current research interests are 1) numerical methods for nonlinear PDEs, for nonlinear partial integro-differential equations and for nonlinear singularly perturbed equations; 2) monotone iterative methods (methods with partial ordering) for solving nonlinear algebraic systems and 3) efficient computational algorithms on parallel computers for modeling physical, chemical and biological systems.