I am a Junior Research Fellow in Mathematics at Trinity College, Oxford.
I am an applied mathematician, specialising in computational mathematics. I have an undergraduate and Masters degrees in Computer Science from IIT Delhi and a Part III in Mathematics from Cambridge. I did my doctoral research in Applied Mathematics at Cambridge, funded by a King’s College Studentship.
My research interests are in the field of computational mathematics, in particular the numerical solution of partial differential equations (PDEs) arising in the physical sciences.
I am currently interested in investigating numerical methods for quantum systems described by a range of equations such as the linear, nonlinear and stochastic versions of the Schrödinger equation, and related equations such as the Pauli, Dirac and Klein–Gordon equations.
I am interested in Lie algebraic techniques such as the Magnus expansion and Zassenhaus splittings, whose combination is very effective for the simulation of equations with time-varying fields and holds great promise for control of quantum systems.
Bader, P., Iserles, A., Kropielnicka, K. and Singh, P., “Efficient methods for linear Schrödinger equation in the semiclassical regime with time-dependent potential”, forthcoming in Proc. Roy. Soc. A.
Singh, P., “Algebraic theory for higher-order methods in computational quantum mechanics”, arXiv:1510.06896 [math.NA], 2015.
Bader, P., Iserles, A., Kropielnicka, K. and Singh, P., “Effective approximation for the linear time-dependent Schrödinger equation”, Found. Comp. Maths 14 (2014), 689-720.