Bibliography#
Alberto Abad, Roberto Barrio, Miguel Marco-Buzunariz, and Marcos Rodríguez. Automatic implementation of the numerical Taylor series method: a Mathematica and Sage approach. Applied Mathematics and Computation, 268:227–245, 2015.
Roberto Barrio. Performance of the Taylor series method for ODEs/DAEs. Applied Mathematics and Computation, 163(2):525–545, 2005.
Luis Benet and David P. Sanders. TaylorSeries.jl: Taylor expansions in one and several variables in Julia. Journal of Open Source Software, 4(36):1043, 2019. URL: https://joss.theoj.org/papers/10.21105/joss.01043, doi:10.21105/joss.01043.
George E. Collins and Alkiviadis G. Akritas. Polynomial real root isolation using Descartes' rule of signs. In Proceedings of the third ACM symposium on Symbolic and algebraic computation, 272–275. 1976.
Alex Haro. Automatic differentiation tools in computational dynamical systems. Univ. of Barcelona Preprint, 2008.
John H. Hubbard. The forced damped pendulum: chaos, complication and control. The American Mathematical Monthly, 106(8):741–758, 1999.
Àngel Jorba and Maorong Zou. A software package for the numerical integration of ODEs by means of high-order Taylor methods. Experimental Mathematics, 14(1):99–117, 2005.
Marcos Rodríguez and Roberto Barrio. Reducing rounding errors and achieving Brouwer's law with Taylor Series Method. Applied Numerical Mathematics, 62(8):1014–1024, 2012.