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Dr Jitse Niesen

Applied Mathematics

Contact details

Room: 9.21
Tel: +44 (0)113 3435870
Email: J.Niesen @


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)


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
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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
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Alnahdi AS, Niesen J, Rucklidge AM Localized patterns in periodically forced systems SIAM Journal on Applied Dynamical Systems, 13, 1311-1327, 2014
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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
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Niesen J, Wright W A Krylov subspace method for option pricing Social Science Research Network, 2011

BÎlǎ N, Niesen J A new class of symmetry reductions for parameter identification problems Journal of Nonlinear Mathematical Physics, 16, 355-371, 2009
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Ledoux V, Malham SJA, Niesen J, Thümmler V Computing stability of multidimensional traveling waves SIAM Journal on Applied Dynamical Systems, 8, 480-507, 2009
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Moan PC, Niesen J Convergence of the magnus series Foundations of Computational Mathematics, 8, 291-301, 2008
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Malham S, Niesen J Evaluating the evans function: Order reduction in numerical methods Mathematics of Computation, 77, 159-179, 2008
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Bîlǎ N, Niesen J On a new procedure for finding nonclassical symmetries Journal of Symbolic Computation, 38, 1523-1533, 2004
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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

Niesen J On the global error committed when evaluating the Evans function numerically.
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Alsallami SAM; Niesen J; Nijhoff FW Closed-form modified Hamiltonians for integrable numerical integration schemes.
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