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#### Two numerical methods for a Caputo fractional-derivative boundary value problem

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**Speaker(s)**Professor Martin Stynes (School of Mathematical Sciences, University College Cork)**Date**From 2014-07-11 To 2014-07-11**Venue**Room 29 at Quan Zhai, BICMR

Speaker: Professor Martin Stynes (School of Mathematical Sciences, University College Cork)

Time: Fri, 07/11/2014 - 16:00

Place: Room 29 at Quan Zhai, BICMR

Abstract: We investigate a linear two-point boundary value problem whose leading term is a Caputo fractional derivative. The problem appears to be simple, but its solution is not well-behaved near one endpoint of the interval, and our interest is in the design and rigorous analysis of numerical methods that take into account this behaviour. To solve numerically the boundary value problem, we present (i) a finite difference method (ii) a spline collocation method.

**Prof. Martin Stynes:**

Martin Stynes is a Professor in School of Mathematical Sciences, at the University College Cork. He is a member of the editorial boards of the journals “Advances in Computational Mathematics”,“Advances in Numerical Analysis”,“Computational Methods in Applied Mathematics” and the “International Journal of Computing Science and Mathematics”. For the period 2003-2005 he was president of the UK/Republic of Ireland Section of SIAM, and he was an editor of SIAM Journal on Numerical Analysis for the period 1998-2003.

He has been interested in the design and analysis of numerical methods for singularly perturbed differential equations. This includes convection-diffusion problems, linearized Navier-Stokes equations and the like. More recently, He has also begun to work on differential equations that contain fractional-order derivatives.

With some of his ideas he opened doors to new developments. Two examples: He proved the first globally uniform convergence result for finite elements applied to a singularly perturbed convection-diffusion problem in 2D(Math.Comp.1991) and he was the first to study finite elements on Shishkin meshes(1994).With his papers (together with B.Kelkogg) on solution decompositions (2006-2008) he created the basis for error estimates for singularly perturbed problems.

Martin is the (co)author of three books. The monograph (together with H.-G.Roos, and L.Tobiska) Numerical Methods for Singularly Perturbed Differential Equations(1996/2008)， and Numerical Treatment of Partial Differential Equations (2007, together with C.Grossmann, H.-G.Roos ).