References
- https://www.dm.uniba.it/testset/testsetivpsolvers
- K. E. Atkinson, An introduction to numerical analysis, John Wiley & Sons, Inc., 1989.
- L. Brugnano, F. Iavernaro and D. Trigiante, Energy- and quadratic invariantspreserving integrators based upon Gauss collocation formulae, SIAM J. Numer. Anal., 50(2012), 2897-2916. https://doi.org/10.1137/110856617
- S. Bu, J. Huang and M. L. Minion, Semi-implicit Krylov deferred correction methods for differential algebraic equations, Math. Comput., 81(280)(2012), 2127-2157. https://doi.org/10.1090/S0025-5718-2012-02564-6
- M. P. Calvo and E. Hairer, Accurate long-term integration of dynamical systems, Appl. Numer. Math., 18(1995), 95-105. https://doi.org/10.1016/0168-9274(95)00046-W
- J. R. Dormand and P. J. Prince, High order embedded Runge-Kutta formulae, J. Comput. Appl. Math., 7(1)(1981), 67-75. https://doi.org/10.1016/0771-050X(81)90010-3
- E. Fehlberg, Classical fifth-, sixth-, seventh-, and eighth-order Runge-Kutta formulas with stepsize control, NASA; for sale by the Clearinghouse for Federal Scientific and Technical Information, Springfield, VA, 1968.
- C. W. Gear, Numerical initial value problems in ordinary differential equations, Prentice-Hall, 1971.
- K. Gustafsson, Control-theoretic techniques for stepsize selection in implicit Runge-Kutta methods, ACM Trans. Math. Softw., 20(4)(1994), 496-517. https://doi.org/10.1145/198429.198437
- E. Hairer, Long-time integration of non-stiff and oscillatory Hamiltonian systems, AIP Conf. Proc., 1168(1)(2009), 3-6.
- E. Hairer, S. P. Norsett and G. Wanner, Solving ordinary differential equations. I nonstiff, Springer Series in Computational Mathematics, Springer, 1993.
- E. Hairer and G. Wanner, Solving ordinary differential equations. II stiff and differential-algebraic problems, Springer Series in Computational Mathematics, Springer, 1996.
- C. Johnson, Error estimates and adaptive time-step control for a class of one-step methods for stiff ordinary differential equations, SIAM J. Numer. Anal., 25(4)(1988), 908-926. https://doi.org/10.1137/0725051
- D. Kavetski, P. Binning and S. W. Sloan, Adaptive time stepping and error control in a mass conservative numerical solution of the mixed form of Richards equation, Adv. Water Resour., 24(2001), 595-605. https://doi.org/10.1016/S0309-1708(00)00076-2
- P. Kim, X. Piao and S. D. Kim, An error corrected Euler method for solving stiff problems based on Chebyshev collocation, SIAM J. Numer. Anal. 49(2011), 2211-2230. https://doi.org/10.1137/100808691
- S. D. Kim, X. Piao, D. H. Kim and P. Kim, Convergence on error correction methods for solving initial value problems, J. Comput. Appl. Math., 236(17)(2012), 4448-4461. https://doi.org/10.1016/j.cam.2012.04.015
- P. Kim, E. Lee and S. D. Kim, Simple ECEM algorithms using function values only, Kyungpook Math. J., 53(2013), 573-591. https://doi.org/10.5666/KMJ.2013.53.4.573
- P. Kim and S. Bu, Error Control Strategy in Error Correction Methods, Kyungpook Math. J., 55(2015), 301-311. https://doi.org/10.5666/KMJ.2015.55.2.301
- G. Y. Kulikov and R. Weiner, Global error estimation and control in linearly-implicit parallel two-step peer W-methods, J. Comput. Appl. Math., 236(2011), 1226-1239. https://doi.org/10.1016/j.cam.2011.08.006
- L. F. Shampine, Error estimation and control for ODEs, J. Sci. Comput., 25(1)(2005), 3-16. https://doi.org/10.1007/s10915-004-4629-3
- L. F. Shampine, Vectorized solution of ODEs in MATLAB, Scalable Comput., Pract. Exp., 10(2010), 337-345.