C1 Lohner Algorithm
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[1] G. Sivashinsky. Nonlinear analysis of hydrodynamic instability in laminar flames—I. Derivation of basic equations , 1977 .
[2] Rage,et al. Rigorous verification of chaos in a molecular model. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.
[3] Y. Kuramoto,et al. Persistent Propagation of Concentration Waves in Dissipative Media Far from Thermal Equilibrium , 1976 .
[4] Martin Berz,et al. New Methods for High-Dimensional Verified Quadrature , 1999, Reliab. Comput..
[5] D Michelson,et al. Steady solutions of the Kuramoto-Sivashinsky equation , 1986 .
[6] S. P. Hastings,et al. A computer proof that the Lorenz equations have “chaotic” solutions , 1994 .
[7] Ernst Hairer,et al. Solving Ordinary Differential Equations I: Nonstiff Problems , 2009 .
[8] W. Tucker. The Lorenz attractor exists , 1999 .
[9] Andreas Griewank,et al. Evaluating derivatives - principles and techniques of algorithmic differentiation, Second Edition , 2000, Frontiers in applied mathematics.
[10] Warwick Tucker,et al. Foundations of Computational Mathematics a Rigorous Ode Solver and Smale's 14th Problem , 2022 .
[11] D. Wilczak,et al. Heteroclinic Connections Between Periodic Orbits in Planar Restricted Circular Three-Body Problem – A Computer Assisted Proof , 2002, math/0201278.
[12] Freddy Dumortier,et al. New aspects in the unfolding of the nilpotent singularity of codimension three , 2001 .
[13] P. Zgliczynski,et al. The existence of simple choreographies for the N-body problem—a computer-assisted proof , 2003, math/0304404.
[14] A. Neumaier. Interval methods for systems of equations , 1990 .
[15] P. Pilarczyk. COMPUTER ASSISTED METHOD FOR PROVING EXISTENCE OF PERIODIC ORBITS , 1999 .
[16] Christopher K McCord. Uniqueness of Connecting Orbits in the Equation Y(3) = Y2 - 1. , 1986 .
[17] Nedialko S. Nedialkov,et al. An Interval Hermite-Obreschkoff Method for Computing Rigorous Bounds on the Solution of an Initial Value Problem for an Ordinary Differential Equation , 1998, SCAN.
[18] Louis B. Rall,et al. Automatic Differentiation: Techniques and Applications , 1981, Lecture Notes in Computer Science.
[19] Yun-Tung Lau. THE "COCOON" BIFURCATIONS IN THREE-DIMENSONAL SYSTEMS WITH TWO FIXED POINTS , 1992 .
[20] Jürgen Moser,et al. Lectures on Celestial Mechanics , 1971 .
[21] D. Wilczak. Chaos in the Kuramoto–Sivashinsky equations—a computer-assisted proof , 2003 .
[22] Jeroen S. W. Lamb,et al. Reversing symmetries in dynamical systems , 1992 .
[23] K. Mischaikow,et al. Chaos in the Lorenz equations: a computer-assisted proof , 1995, math/9501230.
[24] O. Rössler. An equation for continuous chaos , 1976 .
[25] Konstantin Mischaikow,et al. Chaos in the Lorenz equations: A computer assisted proof. Part II: Details , 1998, Math. Comput..
[26] Marian Mrozek,et al. Set arithmetic and the enclosing problem in dynamics , 2000 .
[27] W. Walter. Differential and Integral Inequalities , 1970 .
[28] Konstantin Mischaikow,et al. Rigorous Numerics for Partial Differential Equations: The Kuramoto—Sivashinsky Equation , 2001, Found. Comput. Math..