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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 reaction–diffusion equations, like the Gray–Scott model. The main questions here are how to efficiently evaluate the Evans function, and how to treat two-dimensional problems.

Useful links

Personal web page

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 splittingProceedings 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
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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
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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