Jason Frank

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All published works

Action	Title	Year	Authors
+	Symplectic Runge–Kutta discretization of a regularized forward–backward sweep iteration for optimal control problems	2020	Xin Liu Jason Frank
+ PDF Chat	Derivation of delay equation climate models using the Mori-Zwanzig formalism	2019	Swinda K. J. Falkena Courtney Quinn Jan Sieber Jason Frank Henk A. Dijkstra
+	Symplectic Runge-Kutta discretization of a regularized forward-backward sweep iteration for optimal control problems	2019	Xin Liu Jason Frank
+ PDF Chat	A detectability criterion and data assimilation for nonlinear differential equations	2018	Jason Frank Sergiy Zhuk
+ PDF Chat	Projected Shadowing-Based Data Assimilation	2018	Bart de Leeuw Svetlana Dubinkina Jason Frank Andrew Steyer Xuemin Tu Erik S. Van Vleck
+ PDF Chat	A Note on Statistical Consistency of Numerical Integrators for Multiscale Dynamics	2018	Jason Frank Georg A. Gottwald
+	A detectability criterion and data assimilation for non-linear differential equations	2017	Jason Frank Sergiy Zhuk
+	Projected Shadowing-based Data Assimilation	2017	Bart de Leeuw Svetlana Dubinkina Jason Frank Andrew Steyer Xuemin Tu Erik S. Van Vleck
+ PDF Chat	Exponentially convergent data assimilation algorithm for Navier-Stokes equations	2017	Sergiy Zhuk Tigran Tchrakian Jason Frank
+	Explicit, parallel Poisson integration of point vortices on the sphere	2016	Keith W. Myerscough Jason Frank
+ PDF Chat	Direct control of the small-scale energy balance in two-dimensional fluid dynamics	2015	Jason Frank Benedict Leimkuhler Keith W. Myerscough
+ PDF Chat	Data Assimilation for Linear Parabolic Equations: Minimax Projection Method	2015	Sergiy Zhuk Jason Frank Isabelle Herlin Robert Shorten
+	A separated splitting technique for disconnected rare event sets	2014	Wander Wadman Daan Crommelin Jason Frank
+	Symplectic M&#x00F6;bius integrators for LQ optimal control problems	2014	Jason Frank Sergiy Zhuk
+ PDF Chat	A separated splitting technique for disconnected rare event sets	2014	Wander Wadman Daan Crommelin Jason Frank
+	Least-biased correction of extended dynamical systems using observational data	2014	Keith W. Myerscough Jason Frank Benedict Leimkuhler
+	Applying a splitting technique to estimate electrical grid reliability	2013	Wander Wadman Daan Crommelin Jason Frank
+	Stochastic homogenization for an energy conserving multi-scale toy model of the atmosphere	2013	Jason Frank Georg A. Gottwald
+ PDF Chat	On the multisymplecticity of partitioned Runge–Kutta and splitting methods	2007	Brett N. Ryland Robert I. McLachlan Jason Frank
+ PDF Chat	Conservation of wave action under multisymplectic discretizations	2006	Jason Frank
+ PDF Chat	Linear PDEs and Numerical Methods That Preserve a Multisymplectic Conservation Law	2006	Jason Frank Brian E. Moore Sebastian Reich
+	A note on semi-discrete conservation laws and conservation of wave action by multisymplectic Runge-Kutta box schemes	2006	Jason Frank
+	Energy-conserving semi-discretizations and spurious numerical reflections	2006	Jason Frank Sebastian Reich
+	Conservation of wave action under multisymplectic discretizations	2006	Jason Frank
+	Local conservation and multisymplectic discretizations for PDEs	2006	Jason Frank Brian E. Moore Sebastian Reich Frank Brian E. Moore
+	On spurious reflections, nonuniform grids and finite difference discretizations of wave equations	2004	Jason Frank Sebastian Reich
+ PDF Chat	Geometric space–time integration of ferromagnetic materials	2003	Jason Frank
+	Geometric space-time integration of ferromagnetic materials	2003	Jason Frank
+	On the construction of deflation-based preconditioners	2000	Jason Frank C. Vuik
+ PDF Chat	Geometric Integrators for Classical Spin Systems	1997	Jason Frank Weizhang Huang Benedict Leimkuhler
+	Stability of implicit-explicit linear multistep methods	1996	Jason Frank Willem Hundsdorfer J.G. Verwer

Common Coauthors

Coauthor	Papers Together
Sergiy Zhuk	5
Sebastian Reich	4
Benedict Leimkuhler	3
Daan Crommelin	3
Wander Wadman	3
Keith W. Myerscough	3
Brian E. Moore	2
Xuemin Tu	2
Erik S. Van Vleck	2
Andrew Steyer	2
Bart de Leeuw	2
Svetlana Dubinkina	2
Georg A. Gottwald	2
Xin Liu	2
Henk A. Dijkstra	1
Weizhang Huang	1
Courtney Quinn	1
J.G. Verwer	1
Isabelle Herlin	1
Brett N. Ryland	1
Robert I. McLachlan	1
Jan Sieber	1
Frank	1
C. Vuik	1
Willem Hundsdorfer	1
Robert Shorten	1
Tigran Tchrakian	1
Swinda K. J. Falkena	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations	2009	Ernst Hairer Christian Lubich Gerhard Wanner	11
+	Simulating Hamiltonian Dynamics	2005	Benedict Leimkuhler Sebastian Reich	7
+	Geometric Numerical Integration	2002	Ernst Hairer Gerhard Wanner Christian Lubich	7
+	Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity	2001	Thomas J. Bridges Sebastian Reich	6
+	Multi-Symplectic Runge–Kutta Collocation Methods for Hamiltonian Wave Equations	2000	Sebastian Reich	5
+	Simulating Hamiltonian Dynamics	2005	Benedict Leimkuhler Sebastian Reich	5
+ PDF Chat	Data Assimilation for Linear Parabolic Equations: Minimax Projection Method	2015	Sergiy Zhuk Jason Frank Isabelle Herlin Robert Shorten	5
+	Splitting methods	2002	Robert I. McLachlan G. Quispel	4
+	Symplectic M&#x00F6;bius integrators for LQ optimal control problems	2014	Jason Frank Sergiy Zhuk	4
+ PDF Chat	Controlling instabilities along a 3DVar analysis cycle by assimilating in the unstable subspace: a comparison with the EnKF	2008	Alberto Carrassi A. Trevisan Laurent Descamps Olivier Talagrand Francesco Uboldi	4
+ PDF Chat	On the Compuation of Lyapunov Exponents for Continuous Dynamical Systems	1997	Luca Dieci Robert D. Russell Erik S. Van Vleck	4
+ PDF Chat	Multisymplectic Geometry, Variational Integrators, and Nonlinear PDEs	1998	Jerrold E. Marsden George W. Patrick Steve Shkoller	4
+ PDF Chat	Multisymplectic box schemes and the Korteweg–de Vries equation	2003	Uri M. Ascher Robert I. McLachlan	4
+	Numerical Hamiltonian Problems	1994	J. M. Sanz‐Serna M. P. Calvo	3
+ PDF Chat	Extracting macroscopic dynamics: model problems and algorithms	2004	Dror Givon Raz Kupferman Andrew M. Stuart	3
+	The splitting method in rare event simulation	2000	M.J.J. Garvels	3
+	Data Assimilation: A Mathematical Introduction	2015	Kody J. H. Law Andrew M. Stuart Konstantinos C. Zygalakis	3
+	Symplectic integration of Hamiltonian wave equations	1993	Robert I. McLachlan	3
+ PDF Chat	Data assimilation as a nonlinear dynamical systems problem: Stability and convergence of the prediction-assimilation system	2008	Alberto Carrassi Michael Ghil Anna Trevisan Francesco Uboldi	3
+	Rare Event Simulation using Monte Carlo Methods	2009	Gerardo Rubino Bruno Tuffin	3
+	Construction of higher order symplectic integrators	1990	Haruo Yoshida	3
+ PDF Chat	Solving ordinary differential equations I. nonstiff problems	1987	Ernst Hairer Syvert P. Nørsett Gerhard Wanner	3
+ PDF Chat	Discrete mechanics and variational integrators	2001	Jerrold E. Marsden Matthew West	3
+	A variant of importance splitting for rare event estimation	2011	Michael Amrein Hans R. Künsch	3
+ PDF Chat	Splitting for Rare-Event Simulation	2006	Pierre L’Ecuyer Valérie Demers Bruno Tuffin	3
+ PDF Chat	Thermostats for “Slow” Configurational Modes	2007	A. Samoletov Carl P. Dettmann Mark A. J. Chaplain	2
+	Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Part 1: Theory	1980	Giancarlo Benettin L. Galgani Antonio Giorgilli Jean-Marie Strelcyn	2
+	Synchronization of chaotic systems: Transverse stability of trajectories in invariant manifolds	1997	Reggie Brown Nikolai F. Rulkov	2
+	Group Velocity in Finite Difference Schemes	1982	Lloyd N. Trefethen	2
+	On the importance function in splitting simulation	2002	M.J.J. Garvels Jan‐Kees van Ommeren Dirk P. Kroese	2
+	A limit theorem for perturbed operator semigroups with applications to random evolutions	1973	Thomas G. Kurtz	2
+ PDF Chat	Applications of lie groups to differential equations	1990	Peter J. Olver	2
+ PDF Chat	Genealogical particle analysis of rare events	2005	Pierre Del Moral Josselin Garnier	2
+	Parallel implementation of a multiblock method with approximate subdomain solution	1999	J. Frank C. Vuik	2
+	Anderson Acceleration for Fixed-Point Iterations	2011	Homer F. Walker Peng Ni	2
+ PDF Chat	On the Error in the Product QR Decomposition	2010	Erik S. Van Vleck	2
+	Convergence of the forward-backward sweep method in optimal control	2012	Michael McAsey Libin Mou Weimin Han	2
+ PDF Chat	Riccati Differential Equations	1972	William T. Reid M. R. Chidambara	2
+	Multi-symplectic integration methods for Hamiltonian PDEs	2003	Brian E. Moore Sebastian Reich	2
+ PDF Chat	Geometric space–time integration of ferromagnetic materials	2003	Jason Frank	2
+ PDF Chat	Numerical Shadowing Using Componentwise Bounds and a Sharper Fixed Point Result	2000	Erik S. Van Vleck	2
+ PDF Chat	Lyapunov Exponents and Smooth Ergodic Theory	2001	Luis Barreira Yakov Pesin	2
+ PDF Chat	The role of symplectic integrators in optimal control	2008	Monique Chyba Ernst Hairer Gilles Vilmart	2
+ PDF Chat	Discrete data assimilation in the Lorenz and 2D Navier–Stokes equations	2011	Kevin Hayden Eric J. Olson Edriss S. Titi	2
+ PDF Chat	Riccati Differential Equations	1975	William T. Reid David Jordan	2
+	Energy and group velocity in semi discretizations of hyperbolic equations	1981	Robert Vichnevetsky	2
+	On the numerical computation of orbits of dynamical systems: The higher dimensional case	1992	Shui-Nee Chow Kenneth J. Palmer	2
+ PDF Chat	Geometric Integrators for Classical Spin Systems	1997	Jason Frank Weizhang Huang Benedict Leimkuhler	2
+	Long-Time Asymptotics of the Filtering Distribution for Partially Observed Chaotic Dynamical Systems	2015	Daniel Sanz-Alonso Andrew M. Stuart	2
+ PDF Chat	Numerical Techniques for Approximating Lyapunov Exponents and Their Implementation	2010	Luca Dieci Michael S. Jolly Erik S. Van Vleck	2