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Publications

• L.O. Jay and J. Small: Specialized Runge-Kutta methods for semi-explicit differential-algebraic equations of index 2, 2025. Submitted.
• L.O. Jay and O. Sokratova: Predictors for implicit methods applied with constant step sizes to rescaled differential equations, 2025. Revised submission.
• L.O. Jay: Predictors for implicit symplectic methods applied with constant step sizes to rescaled Hamiltonian systems. In progress.
• L.O. Jay, Q. Chediak, and N. Kapur: Intrinsic projection, starting approximations, and iterative solution of implicit Runge-Kutta type methods for index 3 differential-algebraic equations. In progress.
• L.O. Jay and J.I. Montijano: Analysis of starting approximations for implicit Runge-Kutta methods applied to ODEs based on the reverse method, Appl. Numer. Math., Vol.~215, pp.~1-14, 2025. [online]
• L.O. Jay and O. Sokratova: A note on approximate Jacobians of implicit Runge-Kutta methods and convergence of modified Newton iterations, BIT Numer., Vol. 63, 2023. [online]
• L.O. Jay: Symplecticness conditions of some low order partitioned methods for non-autonomous Hamiltonian systems. Numerical Algorithms. Vol. 86, pp. 495-514, 2021. [online]
• L.O. Jay, B.Ch. Merwine, H. Sugiyama, H. Yamashita: Analysis of a two-stage extension of the generalized-α method for systems in mechanics with holonomic constraints, 2020. This material is based upon work supported by the National Science Foundation under Grant No.0654044. To be resubmitted.
• L.O. Jay, B.Ch. Merwine, H. Sugiyama, H. Yamashita: A two-stage extension of the generalized-α method for constrained systems in mechanics, Proceedings of the ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference IDETC/CIE2020, August 16-19, 2020, St. Louis, MO, USA, DETC2020-22385. This material is based upon work supported by the National Science Foundation under Grant No.0654044.
• D. Yang, J. Huang, and L.O. Jay:: Efficient methods for nonlinear time fractional diffusion-wave equations and their fast implementations. Numerical Algorithms, Vol. 85, pp. 375-397, 2020. [.pdf].
• G. Söderlind, L.O. Jay, and M. Calvo: Stiffness 1952--2012. Sixty years in search of a definition. [online, .pdf]. BIT Numer.. Vol. 55, pp. 531-558, 2015.
• L.F. Shampine and L.O. Jay: Dense output. [online, .pdf]. Encyclopedia of Applied and Computational Mathematics [.pdf], Numerical Analysis of Ordinary Differential Equations, Springer - The Language of Science, Björn Engquist (Ed.), 2015.
• L.O. Jay: Lobatto methods. [online, .pdf]. Encyclopedia of Applied and Computational Mathematics [.pdf], Numerical Analysis of Ordinary Differential Equations, Springer - The Language of Science, Björn Engquist (Ed.), 2015.
• R. Curtu, R. Mantilla, M. Fonley, L.K. Cunha, S.J. Small, L.O. Jay, and W.F. Krajewski: An integral-balance nonlinear model to simulate changes in soil moisture, groundwater, and surface runoff dynamics at the hillslope scale. This material is based upon work supported by the National Science Foundation under Grant No. 1025483. [.pdf]. Advances in Water Resources. Vol. 71, pp. 125-139, 2014.
• S.J. Small, L.O. Jay, R. Mantilla, R. Curtu, L.K. Cunha, M. Fonley, and W.F. Krajewski: An asynchronous solver for systems of ODEs linked by a directed tree structure. This material is based upon work supported by the National Science Foundation under Grant No. 1025483. [.pdf]. Advances in Water Resources. Vol. 53, pp. 23-32, 2013.
• L.O. Jay: Convergence of the generalized-α method for constrained systems in mechanics with nonholonomic constraints. This material is based upon work supported by the National Science Foundation under Grant No.0654044. [ .pdf].
• L.O. Jay and B. Simeon: Consistent extensions of the symplectic Euler method for a class of overdetermined DAEs. This material is based upon work supported by the National Science Foundation under Grant No.0654044. [ .pdf].
• L.O. Jay: Lagrange-d'Alembert SPARK integrators for nonholonomic Lagrangian systems. This material is based upon work supported by the National Science Foundation under Grant No.0654044. [ .pdf]. Submitted.
• L.O. Jay: Preconditioning of implicit Runge-Kutta methods. Scalable Computing: Practice and Experience, Vol. 10, No. 4, pp. 363-372, 2009. This material is based upon work supported by the National Science Foundation under Grant No.0654044. [.pdf]. Addendum for p.366: [.pdf].
• L.O. Jay and D. Negrut: A second order extension of the generalized-α method for constrained systems in mechanics. In "Multibody Dynamics, Computational Methods and Applications", Carlo L. Bottasso ed., Computational Methods in Applied Sciences, E. Onate series ed., Springer, Vol. 12, pp. 143-158, 2008. Special Vol. from ECCOMAS Thematic Conference on Multibody Dynamics held in Milano, 2007. This material is based upon work supported by the National Science Foundation under Grant No.0654044. [ .pdf].
• D. Negrut, L.O. Jay, and N. Khude: A discussion of low-order numerical integration formulas for rigid and flexible multibody dynamics. J. Comput. Nonlinear Dyn., Vol. 4, Issue 2, 021008, 2009. This material is based upon work supported by the National Science Foundation under Grant No.0654044. [.pdf].
• L.O. Jay: Specialized partitioned additive Runge-Kutta methods for systems of overdetermined DAEs with holonomic constraints. SIAM J. Numer. Anal., Vol. 45, pp. 1814-1842, 2007. [.pdf].
• L.O. Jay and D. Negrut: Extensions of the HHT-α method to differential-algebraic equations in mechanics. Electronic Transactions on Numerical Analysis (ETNA), Vol. 26, pp. 190-208, 2007. [.pdf].
• L.O. Jay: Beyond conventional Runge-Kutta methods in numerical integration of ODEs and DAEs by use of structures and local models. J. Comput. Appl. Math., Vol. 204, pp. 56-76, 2007. [.pdf].
• L.O. Jay: Specialized Runge-Kutta methods for index 2 differential algebraic equations. Math. Comput., Vol. 75, pp. 641-654, 2006. [.pdf].
• L.O. Jay: Preserving Poisson structure and orthogonality in numerical integration of differential equations. Comput. Math. Appl., Vol. 48, pp. 237-255, 2004. [.pdf].
• M. Calvo, L.O. Jay, J.I. Montijano, and L. Ràndez: Approximate compositions of a near identity map by multi-revolution Runge-Kutta methods. Numer. Math., Vol. 97, pp. 635-666, 2004. [.pdf].
• S.S. Shome, E.J. Haug, and L.O. Jay: Dual-rate integration using partitioned Runge-Kutta methods for mechanical systems with interacting subsystems. Mech. Based Design Structures Mach., Vol. 32, pp. 253-282, 2004. [.pdf].
• L.O. Jay: Solution of index 2 implicit differential-algebraic equations by Lobatto Runge-Kutta methods. BIT Numer., Vol. 43, pp. 93-106, 2003. [.pdf].
• L.O. Jay: Iterative solution of nonlinear equations for SPARK methods applied to DAEs. Numer. Algorithms, Vol. 31, pp. 171-191, 2002. [.pdf].
• L.O. Jay: A note on Q-order of convergence. BIT Numer., Vol. 41, pp. 422-429, 2001. [.pdf].
• L.O. Jay: Inexact simplified Newton iterations for implicit Runge-Kutta methods. SIAM J. Numer. Anal., Vol. 38, pp. 1369-1388, 2000. [.pdf].
• N. Biehn, S.L. Campbell, L.O. Jay, and T. Westbrook: Some comments on DAE theory for IRK methods and trajectory optimization. J. Comput. Appl. Math., Vol. 120, pp. 109-131, 2000. In a special issue on "SQP-based direct discretization methods for practical optimal control problems". [.pdf].
• P.E. Gill, L.O. Jay, M. W. Leonard, L.R. Petzold, and V. Sharma: An SQP method for the optimal control of large-scale dynamical systems. J. Comput. Appl. Math., Vol. 120, pp. 197-213, 2000. In a special issue on "SQP-based direct discretization methods for practical optimal control problems". [.pdf].
• L.O. Jay and T. Braconnier: A parallelizable preconditioner for the iterative solution of implicit Runge-Kutta type methods. J. Comput. Appl. Math., Vol. 111, pp. 63-76, 1999. [.pdf].
• L.O. Jay, H. Kim, Y. Saad, and J. Chelikowski: Electronic structure calculations for plane-wave codes without diagonalization. Comput. Phys. Comm., Vol. 118, pp. 21-30, 1999. [.pdf].
• L.O. Jay: Structure preservation for constrained dynamics with super partitioned additive Runge-Kutta methods, SIAM J. Sci. Comput., Vol. 20, pp. 416-446, 1998. [.pdf].
• L.R. Petzold, L.O. Jay, and J. Yen: Numerical solution of highly oscillatory ordinary differential equations. Acta Numerica, A. Iserles ed., Cambridge Univ. Press, Cambridge, pp. 437-484, 1997. [.pdf].
• L.O. Jay, A. Sandu, F.A. Potra, and G.R. Carmichael: Improved quasi-steady-state-approximation methods for atmospheric chemistry integration. SIAM J. Sci. Comput., Vol. 18, pp. 182-202, 1997. [.pdf].
• L.R. Petzold, J.B. Rosen, P.E. Gill, L.O. Jay, and K. Park: Numerical optimal control of parabolic PDEs using DASOPT. In "Large-scale optimization with applications", Part II: "Optimal design and control", IMA Vol. Math. Appl., L.T. Biegler, T.F. Coleman, A.R. Conn, and F.N. Santosa eds, Springer, New York, Vol. 93, pp. 271-300, 1997. [.pdf (scanned)].
• L.O. Jay: Symplectic partitioned Runge-Kutta methods for constrained Hamiltonian systems. SIAM J. Numer. Anal., Vol. 33, pp. 368-387, 1996. [.pdf (from JSTOR)].
• L.O. Jay: Convergence of Runge-Kutta methods for differential-algebraic systems of index 3. Appl. Numer. Math., Vol. 17, pp. 97-118, 1995. [.pdf].
• E. Hairer and L.O. Jay: Implicit Runge-Kutta for higher index differential-algebraic systems. Contributions in Numerical Mathematics, World Sci. Ser. Appl. Anal., Vol. 2, pp. 213-224, 1993. [.pdf (scanned)].
• L.O. Jay: Collocation methods for differential-algebraic equations of index 3. Numer. Math., Vol. 65, pp. 407-421, 1993. [.pdf (from Springer Complete Collection)].
• L.O. Jay: Convergence of a class of Runge-Kutta methods for differential-algebraic systems of index 2. BIT Numer., Vol. 33, pp. 137-150, 1993.
[.pdf (from Springer Link)].
• L.O. Jay: Dense output for extrapolation based on the semi-implicit midpoint rule. ZAMM, Vol. 73, pp. 325-329, 1993. [.pdf (scanned)].

Technical reports, preprints, work in progress, etc.

• L.O. Jay and S.J. Small: Lagrange-d'Alembert SPARK integrators for constrained systems in mechanics. To be submitted.
• L.O. Jay and S.J. Small: Specialized partitioned additive Runge-Kutta methods for systems of overdetermined DAEs with mixed index 2 and 3 constraints. In progress.
• L.O. Jay and D.G. Mohr: Curve search and ODEs in nonlinear unconstrained optimization. In progress.
• L.O. Jay: Lagrangian integration with symplectic methods. AHPCRC Preprint 97-009, 1997. [ .pdf].
• L.O. Jay and L.R. Petzold: Highly oscillatory systems and periodic-stability. AHPCRC Preprint 95-015, 1995.
• Ph.D. thesis: Runge-Kutta type methods for index three differential-algebraic equations with applications to Hamiltonian systems. University of Geneva, Department of Mathematics, 1994. [.pdf].
• M.Sc. thesis: Construction of a continuous solution for an extrapolation method: theory and practice. University of Geneva, Department of Mathematics, 1990.

Some conference proceedings papers

• R. Mantilla, L.K. Cunha, W.F. Krajewski, S.J. Small, L.O. Jay, M. Fonley, and R. Curtu: Simulation of a distributed flood control system using a parallel asynchronous solver for systems of ODEs, Proceedings of the IA STED International Conference, Applied Simulation and Modeling (ASM 2012): Artificial Intelligence and Soft Computing, Napoli, Italy, June 25-27, 2012. DOI:10.2316/P.2012.776-042. This material is based upon work supported by the National Science Foundation under grant DMS-1025483. [.pdf].
• D. Negrut, L.O. Jay, A. Tassora, M. Anitescu, H. Mazhar, T. Heyn, and A. Pazouki: Simulation of multibody dynamics leveraging new numerical methods and multiprocessor capabilities. Proceedings of the 2011 NSF CMMI Engineering Research and Innovation Conference, Atlanta, Georgia, January 4-7, 2011. This material is based upon work supported by the National Science Foundation under Grant No.0654044. [.pdf].
• L.O. Jay: On modified Newton iterations for SPARK methods applied to constrained systems in mechanics. This material is based upon work supported by the National Science Foundation under Grant No.0654044. [ .pdf]. Proceedings of the 7th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2009), AIP Conference Proceedings, Th. E. Simos ed. Rethymno, Crete, Greece, September 18-22, pp. 1017-1020, 2009.
• L.O. Jay: Lagrange-d'Alembert SPARK integrators for nonholonomic Lagrangian systems. Proceedings of the 2009 NSF CMMI Engineering Research and Innovation Conference, Honolulu, Hawaii, June 22-25, 2009. This material is based upon work supported by the National Science Foundation under Grant No.0654044. [ .pdf].
• L.O. Jay and D. Negrut: A second order extension of the generalized-α method for constrained systems in mechanics. Proceedings of Multibody Dynamics 2007, ECCOMAS Thematic Conference, C.L. Bottasso, P. Masarati, and L. Trainelli eds., Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano, Milano, Italy, June 25-28, 2007. [ .pdf].
• D. Negrut, L.O. Jay, N. Khude, and T. Heyn: A discussion of low order numerical integration formulas for rigid and flexible multibody dynamics. Proceedings of Multibody Dynamics 2007, ECCOMAS Thematic Conference, C.L. Bottasso, P. Masarati, and L. Trainelli eds., Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano, Milano, Italy, June 25-28, 2007.
• D. Negrut, L.O. Jay, and N. Khude: A discussion of low order numerical integration formulas for rigid and flexible multibody dynamics. Proceedings of IDETC07, Proceedings of the 6th ASME International Conference on Multibody Systems, Nonlinear Dynamics and Control, Las Vegas, Nevada, September 4-7, 2007.
• L.O. Jay: Using additivity in numerical integration of DAEs [.pdf]. Mathematisches ForschungsInstitut Oberwolfach Report 14/2006, pp. 850-853, 2006.
• L.O. Jay: Use of structures and local models in numerical integration of ODEs and DAEs: Beyond traditional Runge-Kutta methods. Proceedings of the International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE-2005, Alicante, Spain, June 27-30, pp. 578-607, 2005.
• Z. Mi, J. Yang, K. Abdel-Malek, and L.O. Jay: Planning for kinematically smooth manipulator trajectories. DETC2002/MECH-34325, Proceedings of 2002 ASME Design Engineering Technical Conferences and Computer and Information in Engineering Conference, 5B, Montreal, Canada, American Society of Mechanical Engineers, New York, pp. 1065-1073, 2002.
• L.O. Jay, A. Sandu, F.A. Potra, and G.R. Carmichael: Efficient numerical integrator for atmospheric chemistry. ICIAM 95, Third International Congress on Industrial and Applied Mathematics, Hamburg, Germany, July 1995. Special Issue of ZAMM, Issue 4: Applied Sciences, E. Kreuzer and O. Mahrenholtz eds., Akademie-Verlag, Berlin, pp. 450-453, 1996.