Efficient Stability-preserving Numerical Methods for Nonlinear Coercive Problems in Vector Space

Speaker:  Wansheng Wang, Shanghai Normal University.

Time:        10:30 am, Dec.5

Location: SIST 1A200

Host:        Qifeng Liao

Abstract:

Strong stability (or monotonicity)-preserving time discretization schemes preserve the stability properties of the exact solution and have proved very useful in scientific and engineering computation, especially in solving hyperbolic partial differential equations. The main aim of this work is to further extend this to exponential stability-preserving numerical methods for general coercive system whose solution is exponentially growing or decaying and the rate of growth or decay can be quantified by a (ω,τ*) function in general vector space with a convex functional. Under the same stepsize condition as for strong stability, sharper exponential stability results are derived for explicit and diagonally implicit Runge-Kutta methods and variable coefficients linear multistep methods for nonlinear problems. The new developments in this paper also include their applications to various linear and nonlinear evolution problems.

Bio:

Wansheng Wang is a professor and doctoral supervisor at Shanghai Normal University, deputy dean of the School of Mathematics and Physics, and director of the Institute of Mathematical Sciences. He mainly engaged in teaching and research on numerical solutions and applications of differential equations, and has achieved a series of results in theoretical analysis and fast algorithms of financial option models, stability-preserving algorithms and adaptive algorithms for differential equations, data assimilation and deep learning algorithms. He has been selected into Hunan Province's New Century 121 Talent Project and Hunan Province's general university subject leaders and other talent plans. He is an editorial board member of AAMM, a director of the China Simulation Society, a standing member of the Financial Technology and Algorithm Committee of the Chinese Society of Industrial and Applied Mathematics, and a member of the China Society of Industrial and Applied Mathematics. Director of the Computational Mathematics Branch of the Mathematical Society.