# School of Mathematics

## Dr Jitse Niesen

Lecturer

Applied Mathematics

### Contact details

Room: 9.21

Tel: +44 (0)113 3435870

Email: J.Niesen @ leeds.ac.uk

### Keywords

Numerical analysis

Geometric numerical integration

Exponential integrators

Matrix functions

Stability of travelling waves

Evans function

## Research interests

At the moment, I am mainly pursuing two topics for research: geometric numerical integration and the numerical evaluation of the Evans function.

Geometric numerical integration is concerned with the construction of numerical algorithms which preserve some of the dynamical properties of the exact solution. Examples of geometric integration methods that I am studying include Magnus methods and exponential integrators.

The Evans function can be used as a tool to analyse the stability of coherent structures for partial differential equations. I am particularly interested in the stability of travelling wave solutions for systems of reactionâ€“diffusion equations, like the Grayâ€“Scott model. The main questions here are how to efficiently evaluate the Evans function, and how to treat two-dimensional problems.

### Useful links

## Current postgraduate students

Shami Alsallami (2014)

Laya Haweil (2013)

Ghadeer Surrati (2017)

Patrick Wright (2014)

## Publications

**Li Y; He Y; Sun Y; Niesen J; Qin H; Liu J ** *Solving Vlasov-Maxwell equations by using Hamiltonian splitting*Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2016 (ICNAAM-2016), 160009 2017

DOI:10.1063/1.4992343

View abstract

**Niesen J, Moan PC** On an asymptotic method for computing the modified energy for symplectic methods *Discrete and Continuous Dynamical Systems - Series A*, **34**, 1105-1120, 2014

DOI:10.3934/dcds.2014.34.1105

View abstract

**Alnahdi AS, Niesen J, Rucklidge AM** Localized patterns in periodically forced systems *SIAM Journal on Applied Dynamical Systems*, **13**, 1311-1327, 2014

DOI:10.1137/130948495

View abstract

**Niesen J, Wright WM** Algorithm 919: A Krylov subspace algorithm for evaluating theψ-functions appearing in exponential integrators *ACM Transactions on Mathematical Software*, **38**, 2012

DOI:10.1145/2168773.2168781

View abstract

**Niesen J, Wright W** A Krylov subspace method for option pricing *Social Science Research Network*, 2011

DOI:10.2139/ssrn.1799124

**BÎlǎ N, Niesen J** A new class of symmetry reductions for parameter identification problems *Journal of Nonlinear Mathematical Physics*, **16**, 355-371, 2009

DOI:10.1142/S1402925109000273

View abstract

**Ledoux V, Malham SJA, Niesen J, Thümmler V** Computing stability of multidimensional traveling waves *SIAM Journal on Applied Dynamical Systems*, **8**, 480-507, 2009

DOI:10.1137/080724009

View abstract

**Moan PC, Niesen J** Convergence of the magnus series *Foundations of Computational Mathematics*, **8**, 291-301, 2008

DOI:10.1007/s10208-007-9010-0

View abstract

**Malham S, Niesen J** Evaluating the evans function: Order reduction in numerical methods *Mathematics of Computation*, **77**, 159-179, 2008

DOI:10.1090/S0025-5718-07-02016-9

View abstract

**Bîlǎ N, Niesen J** On a new procedure for finding nonclassical symmetries *Journal of Symbolic Computation*, **38**, 1523-1533, 2004

DOI:10.1016/j.jsc.2004.07.001

View abstract

**Niesen J** A priori estimates for the global error committed by Runge-Kutta methods for a nonlinear oscillator. *LMS Journal of Computation and Mathematics*, **6**, 18-28, 2003

DOI:10.1112/S1461157000000358

Niesen J On the global error committed when evaluating the Evans function
numerically.

View abstract

Alsallami SAM; Niesen J; Nijhoff FW Closed-form modified Hamiltonians for integrable numerical integration
schemes.

View abstract

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