Title: On the numerical stability of Runge-Kutta methods for Volterra integro-differential equations

Keynote Speaker: Huang Chengming

Abstract:

In this talk, we investigate the stability properties of Runge-Kutta methods for Volterra integro-differential equations. Both the basic and convolution test equations are considered. Some fixed order recurrence relations and the corresponding stability conditions are derived for general methods. The concept of $V_0$-stability is introduced for the convolution test equation and some $V_0$-stable one-stage methods are found. Finally, the $A_0$-stability and $V_0$-stability of the fully implicit discretized collocation methods with one or two stages are investigated in details.

Speaker Introduction:

Huang Chengming, Second-level Professor and Doctoral Supervisor at Huazhong University of Science and Technology; He is mainly engaged in research on numerical calculation of differential equations, and has presided over 5 projects of the National Natural Science Foundation of China, participated in one of the key projects of the National Natural Science Foundation of China, and been selected into the New Century Excellent Talent Support Program of the Ministry of Education in 2005; He has published more than 80 SCI papers in domestic and foreign academic journals such as SIAM Journal on Numerical Analysis, SIAM Journal on Scientific Computing, Numerische Mathematik, IMA Journal of Numerical Analysis, and Journal of Computational Physics. He is also the Executive Director of the Chinese Mathematical Society Computational Branch, Vice Chairman of the Hubei Society of Computational Mathematics, and a member of the Editorial Board of PLOS ONE, Journal on Numerical Methods and Computer Applications, etc.

Inviter:

Zhao Weidong, Professor in School of Mathematics

Time:

June 3 (Monday), 10:00-11:00

Location:

Hall 1032, Block B, Zhixin Building, Central Campus

Hosted by: School of Mathematics, Shandong University