##### Speaker

Dr. Hoang Si Nguyen, Associate Professor, Department of Computing and Mathematics, University of West Georgia

##### Title

Mathematics Seminar Seriestics

##### Subtitle

Generalized explicit pseudo two-step Runge-Kutta-Nystrom methods for solving second-order initial value problems

##### Physical Location

Allen 14

**Abstract: **

A class of explicit pseudo two-step Runge-Kutta-Nystr\"{o}m (GEPTRKN) methods for solving second-order initial value problems

y'' = f(t,y,y'), y(t_0) = y_0, y'(t_0)=y'_0

has been studied. This new class of methods can be considered a generalized version of the class of classical explicit pseudo two-step Runge-Kutta-Nystr\"{o}m methods. We proved that an $s$-stage GEPTRKN method has step order of accuracy $p=s$ and stage order of accuracy $r=s$ for any set of distinct collocation parameters $(c_i)_{i=1}^s$. Super-convergence for order of accuracy of these methods can be obtained if the collocation parameters $(c_i)_{i=1}^s$ satisfy some orthogonality conditions. We proved that an $s$-stage GEPTRKN method can attain order of accuracy $p=s+2$. Numerical experiments have shown that the new methods work better than classical methods for solving non-stiff problems even on sequential computing environments. By their structures, the new methods will be much more efficient when implemented on parallel computers.

**Biosketch: ** Dr. Hoang earned his PhD degree from Kansas State University under the supervision of Prof. A. G. Ramm. Before joining the University of West Georgia, from 2011–2013 he was a visiting assistant professor at University of Oklahoma. His research interests include numerical methods for solving ODEs, PDEs and inverse and ill-posed problems.

For more information, please contact: Dr. Vu Thai Luan at luan@math.msstate.edu.