[A1965]D.G. Anderson, Iterative Procedures for Nonlinear Integral Equations, J. Assoc. Comput. Machinery, 12:547-560, 1965.
[AP1998]U.M Ascher and L.R. Petzold, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, SIAM, Philadelphia, 1998.
[B1985]Bank et al., Transient Simulation of Silicon Devices and Circuits, IEEE Trans. CAD, 4:436-451, 1985.
[B1983]S.R. Billington, Type-Insensitive Codes for the Solution of Stiff and Nonstiff Systems of Ordinary Differential Equations, in: Master Thesis, University of Manchester, United Kingdom, 1983.
[BS1989]P. Bogacki and L.F. Shampine. A 3(2) pair of Runge–Kutta formulas, Appl. Math. Lett., 2:321–325, 1989.
[B1987]P.N. Brown. A local convergence theory for combined inexact-Newton/finite difference projection methods. SIAM J. Numer. Anal., 24:407-434, 1987.
[BBH1989]P.N. Brown, G.D. Byrne and A.C. Hindmarsh. VODE, a Variable-Coefficient ODE Solver. SIAM J. Sci. Stat. Comput., 10:1038-1051, 1989.
[BH1989]P.N. Brown and A.C. Hindmarsh. Reduced Storage Matrix Methods in Stiff ODE Systems. J. Appl. Math. & Comp., 31:49-91, 1989.
[BS1990]P.N. Brown and Y. Saad. Hybrid Krylov Methods for Nonlinear Systems of Equations. SIAM J. Sci. Stat. Comput., 11:450-481, 1990.
[B2008]J.C. Butcher, Numerical Methods for Ordinary Differential Equations. Wiley, 2nd edition, Chicester, England, 2008.
[B1992]G.D. Byrne. Pragmatic Experiments with Krylov Methods in the Stiff ODE Setting. In J.R. Cash and I. Gladwell, editors, Computational Ordinary Differential Equations, pp. 323-356, Oxford University Press, 1992.
[C1979]J.R. Cash. Diagonally Implicit Runge-Kutta Formulae with Error Estimates. IMA J Appl Math, 24:293-301, 1979.
[CK1990]J.R. Cash and A.H. Karp. A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides, ACM Trans. Math. Soft., 16:201-222, 1990.
[CGM2014]J. Cheng, M. Grossman and T. McKercher. Professional Cuda C Programming. John Wiley & Sons, 2014.
[CUDA]NVIDIA CUDA Programming Guide.
[cuSOLVER]NVIDIA cuSOLVER Documentation.
[cuSPARSE]NVIDIA cuSPARSE Documentation.
[DFWBT2010]M.R. Dorr, J.-L. Fattebert, M.E. Wickett, J.F. Belak and P.E.A Turchi. A numerical algorithm for the solution of a phase-field model of polycrystalline materials. J. Comput. Phys., 229(3):626-641, 2010.
[DP1980]J.R. Dormand and P.J. Prince. A family of embedded Runge-Kutta formulae, J. Comput. Appl. Math. 6:19–26, 1980.
[DP2010]T. Davis and E. Palamadai Natarajan. Algortithm 907: KLU, a direct sparse solver for circuit simulation problems. ACM Trans. Math. Soft., 37, 2010.
[DES1982]R.S. Dembo, S.C. Eisenstat and T. Steihaug. Inexact Newton Methods. SIAM J. Numer. Anal., 19:400-408, 1982.
[DGL1999]J.W. Demmel, J.R. Gilbert and X.S. Li. An Asynchronous Parallel Supernodal Algorithm for Sparse Gaussian Elimination. SIAM J. Matrix Analysis and Applications, 20:915-952, 1999.
[DS1996]J.E. Dennis and R.B. Schnabel. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. SIAM, Philadelphia, 1996.
[F2014]R.D. Falgout, S. Friedhoff, TZ.V. Kolev, S.P. MacLachlan, and J.B. Schroder, Parallel Time Integration with Multigrid, SIAM J. Sci. Comput., 36:C635-C661, 2014.
[F2015]R. Falgout and U.M. Yang. Hypre user’s manual. LLNL Technical Report, 2015.
[FS2009]H. Fang and Y. Saad. Two classes of secant methods for nonlinear acceleration. Numer. Linear Algebra Appl., 16:197-21, 2009.
[F1969]E. Fehlberg. Low-order classical Runge-Kutta formulas with step size control and their application to some heat transfer problems. NASA Technical Report 315, 1969.
[F1993]R.W. Freund. A Transpose-Free Quasi-Minimal Residual Algorithm for Non-Hermitian Linear Systems. SIAM J. Sci. Comp., 14:470-482, 1993.
[G1991]K. Gustafsson. Control theoretic techniques for stepsize selection in explicit Runge-Kutta methods. ACM Trans. Math. Soft., 17:533-554, 1991.
[G1994]K. Gustafsson. Control-theoretic techniques for stepsize selection in implicit Runge-Kutta methods. ACM Trans. Math. Soft. 20:496-512, 1994.
[GDL2007]L. Grigori, J.W. Demmel, and X.S. Li. Parallel Symbolic Factorization for Sparse LU with Static Pivoting. SIAM J. Scientific Comptuing, 29:1289-1314, 2007.
[HW1993]E. Hairer, S. Norsett and G. Wanner. Solving Ordinary Differential Equations I. Springer Series in Computational Mathematics, vol. 8, 1993.
[HW1996]E. Hairer and G. Wanner. Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol. 14, 1996.
[HS1952]M.R. Hestenes and E. Stiefel. Methods of Conjugate Gradients for Solving Linear Systems. J. Research of the National Bureau of Standards, 49:409-436, 1952.
[HS1980]K.L. Hiebert and L.F. Shampine. Implicitly Defined Output Points for Solutions of ODEs. Technical Report SAND80-0180, Sandia National Laboratories, February 1980.
[H2000]A.C. Hindmarsh. The PVODE and IDA Algorithms. Technical Report UCRL-ID-141558, LLNL, 2000.
[HS2017]A.C. Hindmarsh and R. Serban. User Documentation for CVODE v5.4.0. Technical Report UCRL-SM-208108, LLNL, 2020.
[HSR2017]A.C. Hindmarsh, R. Serban and D.R. Reynolds. Example Programs for CVODE v5.4.0. Technical Report UCRL-SM-208110, LLNL, 2020.
[HT1998]A.C. Hindmarsh and A.G. Taylor. PVODE and KINSOL: Parallel Software for Differential and Nonlinear Systems. Technical Report UCRL-IL-129739, LLNL, February 1998.
[HK2014]R.D. Hornung and J.A. Keasler. The RAJA Portability Layer: Overview and Status. Technical Report LLNL-TR-661403, LLNL, September 2014.
[JPE2019]S.R. Johnson, A. Prokopenko, and K. J. Evans. Automated Fortran-C++ bindings for Large-Scale Scientific Applications. arXiv:1904.02546 [cs], Apr. 2019.
[K1995]C.T. Kelley. Iterative Methods for Solving Linear and Nonlinear Equations. SIAM, Philadelphia, 1995.
[KC2003]C.A. Kennedy and M.H. Carpenter. Additive Runge-Kutta schemes for convection-diffusion-reaction equations. Appl. Numer. Math., 44:139-181, 2003.
[KC2019]C.A. Kennedy and M.H. Carpenter. Higher-order additive Runge–Kutta schemes for ordinary differential equations. Appl. Numer. Math., 136:183-205, 2019.
[K2004]A. Kv{ae}rno. Singly Diagonally Implicit Runge-Kutta Methods with an Explicit First Stage. BIT Numer. Math., 44:489-502, 2004.
[KLU]KLU Sparse Matrix Factorization Library.
[L2005]X.S. Li. An Overview of SuperLU: Algorithms, Implementation, and User Interface. ACM Trans. Math. Soft., 31:302-325, 2005.
[LD2003]X.S. Li. and J.W. Demmel. A Scalable Distributed-Memory Sparse Direct Solver for Unsymmetric Linear Systems. ACM Trans. Math. Soft., 29:110-140, 2003.
[LWWY2012]P.A. Lott, H.F. Walker, C.S. Woodward and U.M. Yang. An Accelerated Picard Method for Nonlinear Systems Related to Variably Saturated Flow, Adv. Wat. Resour., 38:92-101, 2012.
[oneAPI]Intel oneAPI Programming Guide.
[R2018]D.R. Reynolds. ARKode Example Documentation. Technical Report, Southern Methodist University Center for Scientific Computation, 2020.
[ROCm]AMD ROCm Documentation.
[SS1986]Y. Saad and M.H. Schultz. GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems. SIAM J. Sci. Stat. Comp., 7:856-869, 1986.
[S1993]Y. Saad. A flexible inner-outer preconditioned GMRES algorithm. SIAM J. Sci. Comput., 14:461-469, 1993.
[S2019]A. Sandu, A Class of Multirate Infinitesimal GARK Methods. SIAM J. Numer. Anal., 57:2300-2327, 2019.
[SA2002]A. Sayfy and A. Aburub. Embedded Additive Runge-Kutta Methods. Intern. J. Computer Math., 79:945-953, 2002.
[SKAW2009]M. Schlegel, O. Knoth, M. Arnold, and R. Wolke. Multirate Runge–Kutta schemes for advection equations. J. Comput. Appl. Math., 226:345-357, 2009.
[SKAW2012a]M. Schlegel, O. Knoth, M. Arnold, and R. Wolke. Implementation of multirate time integration methods for air pollution modelling. GMD, 5:1395-1405, 2012.
[SKAW2012b]M. Schlegel, O. Knoth, M. Arnold, and R. Wolke. Numerical solution of multiscale problems in atmospheric modeling. Appl. Numer. Math., 62:1531-1542, 2012.
[S1998]G. Soderlind. The automatic control of numerical integration. CWI Quarterly, 11:55-74, 1998.
[S2003]G. Soderlind. Digital filters in adaptive time-stepping. ACM Trans. Math. Soft., 29:1-26, 2003.
[S2006]G. Soderlind. Time-step selection algorithms: Adaptivity, control and signal processing. Appl. Numer. Math., 56:488-502, 2006.
[SLUUG1999]X.S. Li, J.W. Demmel, J.R. Gilbert, L. Grigori, M. Shao and I. Yamazaki. SuperLU Users’ Guide. 1999.
[SuperLUDIST]SuperLU_DIST Parallel Sparse Matrix Factorization Library.
[SuperLUMT]SuperLU_MT Threaded Sparse Matrix Factorization Library.
[V1992]H.A. Van Der Vorst. Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems. SIAM J. Sci. Stat. Comp., 13:631-644, 1992.
[V1978]J.H. Verner. Explicit Runge-Kutta methods with estimates of the local truncation error. SIAM J. Numer. Anal., 15:772-790, 1978.
[WN2011]H.F. Walker and P. Ni. Anderson acceleration for fixed-point iterations. SIAM J. Numer. Anal., 49:1715-1735, 2011.
[KW1998]O. Knoth and R. Wolke. Implicit-explicit Runge-Kutta methods for computing atmospheric reactive flows. Appl. Numer. Math., 28(2):327-341, 1998.
[XBraid]XBraid: Parallel multigrid in time..
[Z1963]J.A. Zonneveld. Automatic integration of ordinary differential equations. Report R743, Mathematisch Centrum, Postbus 4079, 1009AB Amsterdam, 1963.