References
- R. R. Ahmad, N. Yaacob, A. H. Mohd Murid, Explicit methods in solving stiff ordinary differential equations, Int. J. Comput. Math., 81(2004), 1407-1415. https://doi.org/10.1080/00207160410001661744
- J. Alverez, J. Rojo, An improved class of generalized Runge-Kutta methods for stiff problems. Part I: The scalar case, Appl. Math. Comput., 130(2002), 537-560. https://doi.org/10.1016/S0096-3003(01)00115-1
- J. Alverez, J. Rojo, An improved class of generalized Runge-Kutta methods for stiff problems. Part II: the separated system case, Appl. Math. Comput., 159(2004), 717-758. https://doi.org/10.1016/j.amc.2003.09.023
- K. E. Atkinson, An Introduction to Numerical Analysis, 2nd ed., John Wiley & Sons, NewYork, 1989.
- P. N. Brown, G. D. Byrne, A. C. Hindmarsh, VODE: A variable coefficient ODE solver, SIAM J. Sci. Statist. Comput., 10(1989), 1038-1051. https://doi.org/10.1137/0910062
- J. C. Butcher, Implicit Runge-Kutta processes, Math. Comput., 18(1964), 50-64. https://doi.org/10.1090/S0025-5718-1964-0159424-9
- J. C. Butcher, Integration processes based on Radau quadrature formulas, Math. Comput., 18(1964), 233-244. https://doi.org/10.1090/S0025-5718-1964-0165693-1
- J. C. Butcher, G.Wanner, Runge-Kutta methods: some historical notes, Appl. Numer. Math., 22(1996), 113-151. https://doi.org/10.1016/S0168-9274(96)00048-7
- J. R. Cash, On the integration of stiff systems of ODE's using extended backward differential formulae, Numer. Math., 34(1980), 235-246. https://doi.org/10.1007/BF01396701
- J. R. Cash, S. Considine, An MEBDF code for stiff initial value problems, ACM Trans. Math. Software, 18(2)(1992), 142-155. https://doi.org/10.1145/146847.146922
- C. F. Curtiss, J. O. Hirschfelder, Integration of stiff equations, Proc. Natl. Acad. Sci., 38(1952), 235-243. https://doi.org/10.1073/pnas.38.3.235
- G. Dahlquist, A special stability problem for linear multistep methods, BIT, 3(1963), 27-43. https://doi.org/10.1007/BF01963532
- C. Fredebeul, A-BDF: a generalization of the backward differentiation formulae, SIAM J. Numer. Anal., 35(5)(1998), 1917-1938. https://doi.org/10.1137/S0036142996306217
- N. Guzel, M. Bayram, On the numerical solution of stiff system, Appl. Math. Comput., 170(2005), 230-236. https://doi.org/10.1016/j.amc.2004.11.035
- A. Hadi Alim and A. Khader Error control policy for initial value problems with discontinuities and delays, Kyungpook Math. J., 48(2008), 665-684. https://doi.org/10.5666/KMJ.2008.48.4.665
- E. Hairer, S. P. Norsett, G. Wanner, Solving ordinary differential equations I, Nonstiff problems, Springer Series in Computational Mathematics, Springer 1996.
- E. Hairer, G.Wanner, Solving ordinary differential equations. II. Stiff and differential-algebraic problems, Springer Series in Computational Mathematics, Springer 1996.
- E. Hairer, G.Wanner, Stiff differential equations solved by Radau methods, J. Comput. Appl. Math., 111(1999), 93-111. https://doi.org/10.1016/S0377-0427(99)00134-X
- A. C. Hindmarsh, ODEPACK, A systematized collection of ODE solvers, in: R.S. Stepleman et al., eds, Scientific Computing, North-Holland, Amsterdam, (1983), 55-64.
- L. G. Ixaru, G. V. Berghe, H. D. Meyer, Exponentially fitted variable two-step BDF algorithm for rst order ODEs, Comput. Phys. Comm., 150(2003), 116-128. https://doi.org/10.1016/S0010-4655(02)00676-8
- H. Ramos, J. Vigo-Aguiar, A fourth-order Runge-Kutta method based on BDF-type Chebyshev approximations, J. Comput. Appl. Math., 204(2007), 124-136. https://doi.org/10.1016/j.cam.2006.04.033
- H. Ramos, J. Vigo-Aguiar, An almost L-stable BDF-type method for the numerical solution of stiff ODEs arising from the method of lines, Numer. Methods Partial Differential equations, 23(2007), 1110-1121. https://doi.org/10.1002/num.20212
- H. Ramos, A non-standard explicit integration scheme for initial value problems, Appl. Math. Comput., 189(2007), 710-718. https://doi.org/10.1016/j.amc.2006.11.134
- J. Vigo-Aguiar, H. Ramos, A family of A-stable Runge-Kutta collocation methods of higher order for initial-value problems, IMA J. Numer. Anal., 27(2007), 798-817. https://doi.org/10.1093/imanum/drl040
- J. Vigo-Aguiar, J. Martn-Vaquero, H. Ramos, Exponential tting BDF-Runge-Kutta algorithms, Comput. Phys. Comm., 178(2008), 15-34. https://doi.org/10.1016/j.cpc.2007.07.007
- H. Ramos, R. Carcia-Rubio, Analysis of a Chebyshev-based backward differentiation formulae and realtion with Runge-Kutta collocation methods, Inter. J. Comp. Math., to appear.
- M. M. Stabrowski, An efficient algorithm for solving stiff ordinary differential equations, Simul. Pract. Theory, 5(1997), 333-344. https://doi.org/10.1016/S0928-4869(96)00011-0
- X. Y. Wu, J. L. Xia, Two low accuracy methods for stiff systems, Appl. Math. Comput., 123(2001), 141-153. https://doi.org/10.1016/S0096-3003(00)00010-2
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