Advanced Numerical Differential Equation Solving in the Wolfram Language: References
[ACPR94] Ascher, U., H. Chin, L. Petzold, and S. Reich. "Stabilization of Constrained Mechanical Systems with DAEs and Invariant Manifolds." J. Mech. Struct. Machines 23 (1994): 135–157.
[AP91] Ascher, U. and L. Petzold. "Projected Implicit Runge–Kutta Methods for Differential Algebraic Equations." SIAM J. Numer. Anal. 28 (1991): 1097–1120.
[AP98] Ascher, U. and L. Petzold. Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations. SIAM Press, 1998.
[ARPACK98] Lehoucq, R. B., D. C. Sorensen, and C. Yang. ARPACK Users’ Guide, Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods. SIAM, 1998.
[ATLAS00] Whaley, R. C., A. Petitet, and J. J. Dongarra. "Automated Empirical Optimization of Software and the ATLAS Project." Available electronically from http://math-atlas.sourceforge.net.
[B86] Brown, P. "Decay to Uniform States in Food Webs." SIAM J. Appl. Math. 46 (1986): 376–392.
[BD83] Bader, G. and P. Deuflhard. "A Semi-Implicit Mid-Point Rule for Stiff Systems of Ordinary Differential Equations." Numer. Math 41 (1983): 373–398.
[BS97] Bai, Z. and G. W. Stewart. "SRRIT: a Fortran Subroutine to Calculate the Dominant Invariant Subspace of a Nonsymmetric Matrix." ACM Trans. Math. Soft. 23, no. 4 (1997): 494–513.
[BG94] Benettin, G. and A. Giorgilli. "On the Hamiltonian Interpolation of Near to the Identity Symplectic Mappings with Application to Symplectic Integration Algorithms." J. Stat. Phys. 74 (1994): 1117–1143.
[BZ65] Berezin, I. S. and N. P. Zhidkov. Computing Methods, Volume 2. Pergamon, 1965.
[BM02] Blanes, S. and P. C. Moan. "Practical Symplectic Partitioned Runge–Kutta and Runge–Kutta–Nyström Methods." J. Comput. Appl. Math. 142 (2002): 313–330.
[BCR99a] Blanes, S., F. Casas, and J. Ros. "Symplectic Integration with Processing: A General Study." SIAM J. Sci. Comput. 21 (1999): 711–727.
[BCR99b] Blanes, S., F. Casas, and J. Ros. "Extrapolation of Symplectic Integrators." Report DAMTP NA09, Cambridge University, 1999.
[BS89a] Bogacki, P. and L. F. Shampine. "A 3(2) Pair of Runge–Kutta Formulas." Appl. Math. Letters 2 (1989): 1–9.
[BS89b] Bogacki, P. and L. F. Shampine. "An Efficient Runge–Kutta (4, 5) Pair." Report 89–20, Math. Dept. Southern Methodist University, Dallas, Texas, 1989.
[BGS93] Brankin, R. W., I. Gladwell, and L. F. Shampine. "RKSUITE: A Suite of Explicit Runge–Kutta Codes." In Contributions in Numerical Mathematics, World Scientific, 1993.
[BCP89] Brenan, K., S. Campbell, and L. Petzold. Numerical Solutions of Initial-Value Problems in Differential-Algebraic Equations. Elsevier Science Publishing, 1989.
[BHP94] Brown, P. N., A. C. Hindmarsh, and L. R. Petzold. "Using Krylov Methods in the Solution of Large-Scale Differential-Algebraic Systems." SIAM J. Sci. Comput. 15 (1994): 1467–1488.
[BHP98] Brown, P. N., A. C. Hindmarsh, and L. R. Petzold. "Consistent Initial Condition Calculation for Differential-Algebraic Systems." SIAM J. Sci. Comput. 19 (1998): 1495–1512.
[B87] Butcher, J. C. The Numerical Analysis of Ordinary Differential Equations: Runge–Kutta and General Linear Methods. John Wiley, 1987.
[B90] Butcher, J. C. "Order, Stepsize and Stiffness Switching." Computing. 44, no. 3, (1990): 209–220.
[BS64] Bulirsch, R. and J. Stoer. "Fehlerabschätzungen und Extrapolation mit Rationalen Funktionen bei Verfahren vom Richardson–Typus." Numer. Math. 6 (1964): 413–427.
[CIZ97] Calvo, M. P., A. Iserles, and A. Zanna. "Numerical Solution of Isospectral Flows." Math. Comp. 66, no. 220 (1997): 1461–1486.
[CIZ99] Calvo, M. P., A. Iserles, and A. Zanna. "Conservative Methods for the Toda Lattice Equations." IMA J. Numer. Anal. 19 (1999): 509–523.
[CM95] Campbell, S. L. and E. Moore. "Constraint Preserving Integrators for General Nonlinear Higher Index DAEs." Numer. Math. 69 (1995): 383–399.
[CR91] Candy, J. and R. Rozmus. "A Symplectic Integration Algorithm for Separable Hamiltonian Functions." J. Comput. Phys. 92 (1991): 230–256.
[CH94] Cohen, S. D. and A. C. Hindmarsh. CVODE User Guide. Lawrence Livermore National Laboratory report UCRL-MA-118618, September 1994.
[CH96] Cohen, S. D. and A. C. Hindmarsh. "CVODE, a Stiff/Nonstiff ODE Solver in C." Computers in Physics 10, no. 2 (1996): 138–143.
[CKL04] Chowdhary, S., H. Krendl, and A. Linninger. "Symbolic-Numeric Index Analysis Algorithm for Differential Algebraic Equations." Ind. Eng. Chem. Res. 43 (2004): 3886–3894.
[C87] Cooper, G. J. "Stability of Runge–Kutta Methods for Trajectory Problems." IMA J. Numer. Anal. 7 (1987): 1–13.
[DP80] Dormand, J. R. and P. J. Prince. "A Family of Embedded Runge–Kutta Formulae." J. Comp. Appl. Math. 6 (1980): 19–26.
[DL01] DelBuono, N. and L. Lopez. "Runge–Kutta Type Methods Based on Geodesics for Systems of ODEs on the Stiefel Manifold." BIT 41, no. 5 (2001): 912–923.
[D83] Deuflhard, P. "Order and Step Size Control in Extrapolation Methods." Numer. Math. 41 (1983): 399–422.
[D85] Deuflhard, P. "Recent Progress in Extrapolation Methods for Ordinary Differential Equations." SIAM Rev. 27 (1985): 505–535.
[DN87] Deuflhard, P. and U. Nowak. "Extrapolation Integrators for Quasilinear Implicit ODEs." In Large-Scale Scientific Computing. Birkhäuser, 1987.
[DS93] Duff, I. S. and J. A. Scott. "Computing Selected Eigenvalues of Sparse Unsymmetric Matrices Using Subspace Iteration." ACM Trans. Math. Soft. 19, no. 2, (1993): 137–159.
[DHZ87] Deuflhard, P., E. Hairer, and J. Zugck. "One-Step and Extrapolation Methods for Differential-Algebraic Systems." Numer. Math. 51 (1987): 501–516.
[DRV94] Dieci, L., R. D. Russel, and E. S. Van Vleck. "Unitary Integrators and Applications to Continuous Orthonormalization Techniques." SIAM J. Num. Anal. 31 (1994): 261–281.
[DV99] Dieci, L. and E. S. Van Vleck. "Computation of Orthonormal Factors for Fundamental Solution Matrices." Numer. Math. 83 (1999): 599–620.
[DLP98a] Diele, F., L. Lopez, and R. Peluso. "The Cayley Transform in the Numerical Solution of Unitary Differential Systems." Adv. Comput. Math. 8 (1998): 317–334.
[DLP98b] Diele, F., L. Lopez, and T. Politi. "One Step Semi-Explicit Methods Based on the Cayley Transform for Solving Isospectral Flows." J. Comput. Appl. Math. 89 (1998): 219–223.
[ET92] Earn, D. J. D. and S. Tremaine. "Exact Numerical Studies of Hamiltonian Maps: Iterating without Roundoff Error." Physica D. 56 (1992): 1–22.
[F69] Fehlberg, E. "Low-Order Classical Runge–Kutta Formulas with Step Size Control and Their Application to Heat Transfer Problems." NASA Technical Report 315, 1969 (extract published in Computing 6 (1970): 61–71).
[F88] Filippov, A. Differential Equations with Discontinuous Right Hand Sides. Kluwer Academic Publishers, 1988.
[FR90] Forest, E. and R. D. Ruth. "Fourth Order Symplectic Integration." Physica D. 43 (1990): 105–117.
[F92] Fornberg, B. "Fast Generation of Weights in Finite Difference Formulas." In Recent Developments in Numerical Methods and Software for ODEs/DAEs/PDEs. World Scientific, 1992.
[F96a] Fornberg, B. A Practical Guide to Pseudospectral Methods. Cambridge University Press, 1996.
[F98] Fornberg, B. "Calculation of Weights in Finite Difference Formulas." SIAM Review 40, no. 3 (1998): 685–691 (Available in PDF).
[F96b] Fukushima, T. "Reduction of Round-off Errors in the Extrapolation Methods and its Application to the Integration of Orbital Motion." Astron. J. 112, no. 3 (1996): 1298–1301.
[G51] Gill, S. "A Process for the Step-by-Step Integration of Differential Equations in an Automatic Digital Computing Machine." Proc. Cambridge Philos. Soc. 47 (1951): 96–108.
[G65] Gragg, W. B. "On Extrapolation Algorithms for Ordinary Initial Value Problems." SIAM J. Num. Anal. 2 (1965): 384–403.
[GØ84] Gear, C. W. and O. Østerby. "Solving Ordinary Differential Equations with Discontinuities." ACM Trans. Math. Soft. 10 (1984): 23–44.
[G91] Gustafsson, K. "Control Theoretic Techniques for Stepsize Selection in Explicit Runge–Kutta Methods." ACM Trans. Math. Soft. 17, (1991): 533–554.
[G94] Gustafsson, K. "Control Theoretic Techniques for Stepsize Selection in Implicit Runge–Kutta Methods." ACM Trans. Math. Soft. 20, (1994): 496–517.
[GMW81] Gill, P., W. Murray, and M. Wright. Practical Optimization. Academic Press, 1981.
[GDC91] Gladman, B., M. Duncan, and J. Candy. "Symplectic Integrators for Long-Term Integrations in Celestial Mechanics." Celest. Mech. 52 (1991): 221–240.
[GSB87] Gladwell, I., L. F. Shampine and R. W. Brankin. "Automatic Selection of the Initial Step Size for an ODE Solver." J. Comp. Appl. Math. 18 (1987): 175–192.
[GVL96] Golub, G. H. and C. F. Van Loan. Matrix Computations. (3rd ed.) Johns Hopkins University Press, 1996.
[H94] Hairer, E. "Backward Analysis of Numerical Integrators and Symplectic Methods." Annals of Numerical Mathematics 1 (1984): 107–132.
[H97] Hairer, E. "Variable Time Step integration with Symplectic Methods." Appl. Numer. Math. 25 (1997): 219–227.
[H00] Hairer, E. "Symmetric Projection Methods for Differential Equations on Manifolds." BIT 40, no. 4 (2000): 726–734.
[HL97] Hairer, E. and Ch. Lubich. "The Life-Span of Backward Error Analysis for Numerical Integrators." Numer. Math. 76 (1997): 441–462. Erratum: http://www.unige.ch/math/folks/hairer.
[HL88a] Hairer, E. and Ch. Lubich. "Extrapolation at Stiff Differential Equations." Numer. Math. 52 (1988): 377–400.
[HL88b] Hairer, E. and Ch. Lubich. "On Extrapolation Methods for Stiff and Differential-Algebraic Equations." Teubner Texte zur Mathematik 104 (1988): 64–73.
[HLR89] Hairer, E., C. Lubich, and M. Roche. "The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods." Lecture Notes in Mathematics 1409 (1989): 139–.
[HO90] Hairer, E. and A. Ostermann. "Dense Output for Extrapolation Methods." Numer. Math. 58 (1990): 419–439.
[HW96] Hairer, E. and G. Wanner, Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems. (2nd ed.) Springer-Verlag, 1996.
[HW99] Hairer, E. and G. Wanner. "Stiff Differential Equations Solved by Radau Methods." J. Comp. Appl. Math. 111 (1999): 93–111.
[HLW02] Hairer, E., Ch. Lubich, and G. Wanner. Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations. Springer-Verlag, 2002.
[HNW93] Hairer, E., S. P. Nørsett, and G. Wanner. Solving Ordinary Differential Equations I: Nonstiff Problems. (2nd ed.) Springer-Verlag, 1993.
[H97] Higham, D. "Time-Stepping and Preserving Orthonormality." BIT 37, no. 1 (1997): 24–36.
[H89] Higham, N. J. "Matrix Nearness Problems and Applications." In Applications of Matrix Theory. Oxford University Press, 1989.
[H96] Higham, N. J. Accuracy and Stability of Numerical Algorithms. SIAM, 1996.
[H83] Hindmarsh, A. C. "ODEPACK, A Systematized Collection of ODE Solvers." In Scientific Computing, Vol. 1 of IMACS Transactions on Scientific Computation. North-Holland, 1983.
[HT99] Hindmarsh, A. and A. Taylor. User Documentation for IDA: A Differential-Algebraic Equation Solver for Sequential and Parallel Computers. Lawrence Livermore National Laboratory report, UCRL-MA-136910, December 1999.
[KL97] Kahan, W. H. and R. C. Li. "Composition Constants for Raising the Order of Unconventional Schemes for Ordinary Differential Equations." Math. Comp. 66 (1997): 1089–1099.
[K65] Kahan, W. H. "Further Remarks on Reducing Truncation Errors." Comm. ACM. 8 (1965): 40.
[K93] Koren, I. Computer Arithmetic Algorithms. Prentice Hall, 1993.
[L87] Lambert, J. D. Numerical Methods for Ordinary Differential Equations. John Wiley, 1987.
[LS96] Lehoucq, R. B and J. A. Scott. "An Evaluation of Software for Computing Eigenvalues of Sparse Nonsymmetric Matrices." Preprint MCS-P547-1195, Argonne National Laboratory, 1996.
[LPG91] Leimkhular, B. J., L. R. Petzold, and C. W. Gear. "Approximation Methods for the Consistent Initialization of Differential Algebraic Equations." SIAM Journal of Num. Anal. 28 (1991): 205–226.
[LAPACK99] Anderson, E., Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorenson. LAPACK Users' Guide. (3rd ed.) SIAM, 1999.
[M68] Marchuk, G. "Some Applications of Splitting-Up Methods to the Solution of Mathematical Physics Problems." Aplikace Matematiky 13 (1968): 103–132.
[MR99] Marsden, J. E. and T. Ratiu. Introduction to Mechanics and Symmetry: Texts in Applied Mathematics, Vol. 17. (2nd ed.) Springer-Verlag, 1999.
[M93] McLachlan, R. I. "Explicit Lie–Poisson Integration and the Euler Equations." Phys. Rev. Lett. 71 (1993): 3043–3046.
[M95a] McLachlan, R. I. "On the Numerical Integration of Ordinary Differential Equations by Symmetric Composition Methods." SIAM J. Sci. Comp. 16 (1995): 151–168.
[M95b] McLachlan, R. I. "Composition Methods in the Presence of Small Parameters." BIT 35 (1995): 258–268.
[M01] McLachlan, R. I. "Families of High-Order Composition Methods." Numerical Algorithms 31 (2002): 233–246.
[MA92] McLachlan, R. I. and P. Atela. "The Accuracy of Symplectic Integrators." Nonlinearity 5 (1992): 541–562.
[MQ02] McLachlan, R. I. and G. R. W. Quispel. "Splitting Methods." Acta Numerica 11 (2002): 341–434.
[MG80] Mitchell, A. and D. Griffiths. The Finite Difference Method in Partial Differential Equations. John Wiley and Sons, 1980.
[M65a] Møller, O. "Quasi Double-Precision in Floating Point Addition." BIT 5 (1965): 37–50.
[M65b] Møller, O. "Note on Quasi Double-Precision." BIT 5 (1965): 251–255.
[M97] Murua, A. "On Order Conditions for Partitioned Symplectic Methods." SIAM J. Numer. Anal. 34, no. 6 (1997): 2204–2211.
[MM08] Mazzia. F. and C. Magherini, "Test Set for Initial Value Problem Solvers-Release 2.4." Dept. of Mathematics, University of Vari and INdAM, Research Unit of Bari. 2008.
[MS93] Mattson, S. and G. Söderlind. "Index Reduction in Differential-ALgebraic Equations Using Dummy Derivatives." SIAM J. Sci Comput. 14, no. 3: 677–692.
[MS99] Murua, A. and J. M. Sanz-Serna. "Order Conditions for Numerical Integrators Obtained by Composing Simpler Integrators." Phil. Trans. Royal Soc. A 357 (1999): 1079–1100.
[M04] Moler, C. B. Numerical Computing with MATLAB. SIAM, 2004.
[Na79] Na, T. Y. Computational Methods in Engineering: Boundary Value Problems. Academic Press, 1979.
[NP05] Nedialkov, N. and J. Pryce "Solving Differential Algebraic Equations by Taylor Series (I): Computing Taylor Coefficients." BIT 45, no.3 (2005): 561–591.
[N93] Nobel, A. "CBS-Reaction Meeting Koln-Handouts." Br/ARLO-CRC 1993.
[OS92] Okunbor, D. I. and R. D. Skeel. "Explicit Canonical Methods for Hamiltonian Systems." Math. Comp. 59 (1992): 439–455.
[O95] Olsson, H. "Practical Implementation of Runge–Kutta Methods for Initial Value Problems." Licentiate thesis, Department of Computer Science, Lund University, 1995.
[O98] Olsson, H. "Runge–Kutta Solution of Initial Value Problems: Methods, Algorithms and Implementation." PhD Thesis, Department of Computer Science, Lund University, 1998.
[OS00] Olsson, H. and G. Söderlind. "The Approximate Runge–Kutta Computational Process." BIT 40, no. 2 (2000): 351–373.
[P83] Petzold, L. R. "Automatic Selection of Methods for Solving Stiff and Nonstiff Systems of Ordinary Differential Equations." SIAM J. Sci. Stat. Comput. 4 (1983): 136–148.
[P88] Pantelides, C. "The Consistent Initialization of Differential-Algebraic Equations." SIAM J Sci. Stat. Comput. 9, no. 2: 213–231.
[QSS00] Quarteroni, A., R. Sacco, and F. Saleri. Numerical Mathematics. Springer-Verlag, 2000.
[QV94] Quarteroni, A. and A. Valli. Numerical Approximation of Partial Differential Equations. Springer-Verlag, 1994.
[QT90] Quinn, T. and S. Tremaine. "Roundoff Error in Long-Term Planetary Orbit Integrations." Astron. J. 99, no. 3 (1990): 1016–1023.
[R93] Reich, S. "Numerical Integration of the Generalized Euler Equations." Tech. Rep. 93–20, Dept. Comput. Sci. Univ. of British Columbia, 1993.
[R99] Reich, S. "Backward Error Analysis for Numerical Integrators." SIAM J. Num. Anal. 36 (1999): 1549–1570.
[R98] Rubinstein, B. "Numerical Solution of Linear Boundary Value Problems." Mathematica MathSource package, http://library.wolfram.com/database/MathSource/2127.
[RM57] Richtmeyer, R. and K. Morton. Difference Methods for Initial Value Problems. Krieger Publishing Company, 1994 (original edition 1957).
[R87] Robertson, B. C. "Detecting Stiffness with Explicit Runge–Kutta Formulas." Report 193/87, Dept. Comp. Sci., University of Toronto, 1987.
[S84b] Saad, Y. "Chebyshev Acceleration Techniques for Solving Nonsymmetric Eigenvalue Problems." Math. Comp. 42, (1984): 567–588.
[SC94] Sanz-Serna J. M. and M. P. Calvo. Numerical Hamiltonian Problems: Applied Mathematics and Mathematical Computation, No. 7. Chapman and Hall, 1994.
[S91] Schiesser, W. The Numerical Method of Lines. Academic Press, 1991.
[S77] Shampine, L. F. "Stiffness and Non-Stiff Differential Equation Solvers II: Detecting Stiffness with Runge-Kutta Methods." ACM Trans. Math. Soft. 3, no. 1 (1977): 44–53.
[S83] Shampine, L. F. "Type-Insensitive ODE Codes Based on Extrapolation Methods." SIAM J. Sci. Stat. Comput. 4, no. 4 (1983): 635–644.
[S84a] Shampine, L. F. "Stiffness and the Automatic Selection of ODE Code." J. Comp. Phys. 54, no. 1 (1984): 74–86.
[S86] Shampine, L. F. "Conservation Laws and the Numerical Solution of ODEs." Comp. Maths. Appl. 12B (1986): 1287–1296.
[S87] Shampine, L. F. "Control of Step Size and Order in Extrapolation Codes." J. Comp. Appl. Math. 18 (1987): 3–16.
[S91] Shampine, L. F. "Diagnosing Stiffness for Runge-Kutta Methods." SIAM J. Sci. Stat. Comput. 12, no. 2 (1991): 260–272.
[S94] Shampine, L. F. Numerical Solution of Ordinary Differential Equations. Chapman and Hall, 1994.
[S02] Shampine, L. F. "Solving in Matlab." Journal of Numerical Mathematics 10, no. 4 (2002): 291–310.
[SB83] Shampine, L. F. and L. S. Baca. "Smoothing the Extrapolated Midpoint Rule." Numer. Math. 41 (1983): 165–175.
[SG75] Shampine, L. F. and M. Gordon. Computer Solutions of Ordinary Differential Equations. W. H. Freeman, 1975.
[SR97] Shampine, L. F. and M. W. Reichelt. "The MATLAB ODE Suite." SIAM J. Sci. Comp. 18, no. 1 (1997): 1–22.
[ST00] Shampine, L. F. and S. Thompson. "Solving Delay Differential Equations with dde23." Available electronically from http://www.runet.edu/~thompson/webddes/tutorial.pdf.
[ST01] Shampine, L. F. and S. Thompson. "Solving DDEs in MATLAB." Appl. Numer. Math. 37 (2001): 441–458.
[SGT03] Shampine, L. F., I. Gladwell, and S. Thompson. Solving ODEs with MATLAB. Cambridge University Press, 2003.
[SBB83] Shampine, L. F., L. S. Baca, and H. J. Bauer. "Output in Extrapolation Codes." Comp. and Maths. with Appl. 9 (1983): 245–255.
[SS03] Sofroniou, M. and G. Spaletta. "Increment Formulations for Rounding Error Reduction in the Numerical Solution of Structured Differential Systems." Future Generation Computer Systems 19, no. 3 (2003): 375–383.
[SS04] Sofroniou, M. and G. Spaletta. "Construction of Explicit Runge–Kutta Pairs with Stiffness Detection." Mathematical and Computer Modelling, special issue on The Numerical Analysis of Ordinary Differential Equations, 40, no. 11–12 (2004): 1157–1169.
[SS05] Sofroniou, M. and G. Spaletta. "Derivation of Symmetric Composition Constants for Symmetric Integrators." Optimization Methods and Software 20, no. 4–5 (2005): 597–613.
[SS06] Sofroniou, M. and G. Spaletta. "Hybrid Solvers for Splitting and Composition Methods." J. Comp. Appl. Math., special issue from the International Workshop on the Technological Aspects of Mathematics, 185, no. 2 (2006): 278–291.
[S84c] Sottas, G. "Dynamic Adaptive Selection Between Explicit and Implicit Methods When Solving ODEs." Report, Sect. de math, University of Genève, 1984.
[S07] Sprott, J. C. "A Simple Chaotic Delay Differential Equation." Phys. Lett. A. 366 (2007): 397-402.
[S68] Strang, G. "On the Construction of Difference Schemes." SIAM J. Num. Anal. 5 (1968): 506–517.
[S70] Stetter, H. J. "Symmetric Two-Step Algorithms for Ordinary Differential Equations." Computing 5 (1970): 267–280.
[S01] Stewart, G. W. "A Krylov-Schur Algorithm for Large Eigenproblems." SIAM J. Matrix Anal. Appl. 23, no. 3, (2001): 601-614.
[SJ81] Stewart, W. J. and A. Jennings. "LOPSI: A Simultaneous Iteration Method for Real Matrices." ACM Trans. Math. Soft. 7, no. 2, (1981): 230–232.
[S90] Suzuki, M. "Fractal Decomposition of Exponential Operators with Applications to Many-Body Theories and Monte Carlo Simulations." Phys. Lett. A 146 (1990): 319–323.
[SLEPc05] Hernandez, V., J. E. Roman, and V. Vidal. "SLEPC: A Scalable and Flexible Toolkit for the Solution of Eigenvalue Problems." ACM Trans. Math. Soft. 31, no. 3 (2005): 351–362.
[T59] Trotter, H. F. "On the Product of Semi-Group Operators." Proc. Am. Math. Soc. 10 (1959): 545–551.
[TZ08] Tang, X. H. and X. Zou. "Global Attractivity in a Predator-Prey System with Pure Delays." Proc. Edinburgh Math. Soc. 51, 495-508, 2008.
[UKM95] Unger, J., A. Kroner, and W. Marquardt. "Structural Analysis of Differential Algebraic Equation Systems—Theory and Applications." Computers Chem. Engg. 19, no. 8 (1995): 867–882.
[V10] Verner, J. H. "Numerically Optimal Runge-Kutta Pairs with Interpolants." Numerical. Algorithms. 53 (2010): 383–396.
[V79] Vitasek, E. "A-Stability and Numerical Solution of Evolution Problems." IAC 'Mauro Picone', Series III 186 (1979): 42.
[W76] Whitham, G. B. Linear and Nonlinear Waves. John Wiley and Sons, 1976.
[WH91] Wisdom, J. and M. Holman. "Symplectic Maps for the N-Body Problem." Astron. J. 102 (1991): 1528–1538.
[Y90] Yoshida, H. "Construction of High Order Symplectic Integrators." Phys. Lett. A. 150 (1990): 262–268.
[Z98] Zanna, A. "On the Numerical Solution of Isospectral Flows." PhD thesis, Cambridge University, 1998.
[Z72] Zeeman, E. C. "Differential Equations for the Heartbeat and Nerve Impulse." In Towards a Theoretical Biology. Edinburgh University Press, 1972.
[Z06] Zennaro, M. "The Numerical Solution of Delay Differential Equations." Lecture notes, Dobbiaco Summer School on Delay Differential Equations and Applications, 2006.