Geometric Numerical Integration References

Douglas N. Arnold. Numerical Analysis and Scientific Computing. University of Minnesota, 2015-2016. Chapter 1 Interpolation and Approximation, Chapter 2 Numerical Quadrature. (Author's Web Site)
Ernst Hairer and Christian Lubich. Numerical Solution of Ordinary Differential Equations. The Princeton Companion to Applied Mathematics, 293-305, 2015. Princeton University Press. (Author's Web Site)
Ernst Hairer, Christian Lubich and Gerhard Wanner. Geometric Numerical Integration Illustrated by the Störmer–Verlet Method. Acta Numerica 12, 399-450, 2003. (Journal)
Adrián J. Lew and Pablo Mata: A Brief Introduction to Variational Integrators. Structure-preserving Integrators in Nonlinear Structural Dynamics and Flexible Multibody Dynamics, 201-291, 2016. (Journal)
Alain Bossavit. Applied Differential Geometry: A Compendium. (Author's Web Site)

Tevian Dray. Differential Forms and the Geometry of General Relativity. CRC Press, 2014.
Shigeyuki Morita （森田茂之）. Geometry of Differential Forms（微分形式の幾何学）. American Mathematical Society, 2001.
Richard W. R. Darling. Differential Forms and Connections. Cambridge University Press, 1994.

Jeffrey M. Lee. Manifolds and Differential Geometry. American Mathematical Society, 2009.
John M. Lee. Introduction to Smooth Manifolds. Springer, 2013. (eBook)
Loring W. Tu. An Introduction to Manifolds. Springer, 2011. (eBook)
Ralph Abraham, Jerrold E. Marsden and Tudor S. Ratiu. Manifolds, Tensor Analysis, and Applications. Springer, 1988. (eBook)
Michael Spivak. A Comprehensive Introduction to Differential Geometry. Publish or Perish, 1999.

John Baez and Javier P. Muniain. Gauge Fields, Knots and Gravity. World Scientific, 1994.
Gerardo F. Torres del Castillo. Differentiable Manifolds: A Theoretical Physics Approach. Birkhäuser, 2012. (eBook)
Mikio Nakahara. Geometry, Topology and Physics. CRC Press, 2003.
Theodore Frankel. The Geometry of Physics. Cambridge University Press, 2011.

Jorge V. José and Eugene J. Saletan. Classical Dynamics. Cambridge University Press, 1998.
Vladimir I. Arnol’d. Mathematical Methods of Classical Mechanics. Springer, 1989. (eBook)
Jerrold E. Marsden and Tudor S. Ratiu. Introduction to Mechanics and Symmetry. Springer, 1999. (eBook)
Ralph Abraham and Jerrold E. Marsden. Foundations of Mechanics. Addison-Wesley, 1987. (eBook)

Douglas N. Arnold. Numerical Analysis and Scientific Computing. University of Minnesota, 2015-2016. (Author's Web Site)
Douglas N. Arnold. A Concise Introduction to Numerical Analysis. Penn State University, 2001. (Author's Web Site)
Alfio Quarteroni, Riccardo Sacco and Fausto Saleri. Numerical Mathematics. Springer, 2007. (eBook)
Walter Gautschi: Numerical Analysis: An Introduction. Birkhäuser, 2012. (eBook)
Peter Deuflhard, Andreas Hohmann. Numerical Analysis in Modern Scientific Computing. Springer, 2003. (eBook)
Kendall Atkinson and Weimin Han. Theoretical Numerical Analysis: A Functional Analysis Framework. Springer, 2009. (eBook)

Ernst Hairer and Christian Lubich. Numerical Solution of Ordinary Differential Equations. The Princeton Companion to Applied Mathematics, 293-305, 2015. Princeton University Press. (Author's Web Site)
Ernst Hairer, Syvert P. Nørsett and Gerhard Wanner. Solving Ordinary Differential Equations I: Nonstiff Problems. Springer, 1993. (eBook)
Ernst Hairer and Gerhard Wanner. Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems. Springer, 1996. (eBook)
Peter Deuflhard, Folkmar Bornemann. Scientific Computing with Ordinary Differential Equations. Springer, 2002. (eBook)
John C. Butcher. Numerical Methods for Ordinary Differential Equations. Wiley, 2016.

Ernst Hairer, Christian Lubich and Gerhard Wanner. Geometric Numerical Integration Illustrated by the Störmer–Verlet Method. Acta Numerica 12, 399-450, 2003. (Journal)
Ernst Hairer, Christian Lubich and Gerhard Wanner. Geometric Numerical Integration. Springer, 2006. (eBook)
Benedict Leimkuhler and Sebastian Reich. Simulating Hamiltonian Dynamics. Cambridge University Press, 2005. (eBook)
Sergio Blanes, Fernando Casas. A Concise Introduction to Geometric Numerical Integration. CRC Press, 2016.

Adrián J. Lew and Pablo Mata: A Brief Introduction to Variational Integrators. Structure-preserving Integrators in Nonlinear Structural Dynamics and Flexible Multibody Dynamics, 201-291, 2016. (Journal)
Jerrold E. Marsden and Matthew West. Discrete Mechanics and Variational Integrators. Acta Numerica Volume 10, 357-514, 2001. (Journal)
Jerrold E. Marsden, George W. Patrick, Steve Shkoller: Multisymplectic Geometry, Variational Integrators, and Nonlinear PDEs. Communications in Mathematical Physics Volume 199, 351–395, 1998). (Journal)

Sebastian Reich. Backward Error Analysis for Numerical Integrators. SIAM Journal on Numerical Analysis 36, 1549-1570, 1999. (Journal)
Ernst Hairer. Backward Error Analysis for Multistep Methods. Numerische Mathematik 84, 199-232, 1999. (Journal)

Mats G. Larson and Fredrik Bengzon: The Finite Element Method. Theory, Implementation, and Applications. Springer, 2013. (eBook)
Daniele Boffi, Franco Brezzi, Michel Fortin: Mixed Finite Element Methods and Applications. Springer, 2013. (eBook)
Jan S. Hesthaven, Tim Warburton: Nodal Discontinuous Galerkin Methods. Springer, 2008. (eBook)

Robert Johansson. Lectures on Scientific Computing with Python. (GitHub)
Anthony Scopatz and Kathryn D. Huff. Effective Computation in Physics. O'Reilly, 2015. (Safari Books)
Hans Petter Langtangen. A Primer on Scientific Programming with Python. Springer, 2014. (eBook)

Mark Lutz. Learning Python. O'Reilly, 2013. (Safari Books)
Luciano Ramalho. Fluent Python. O'Reilly, 2015. (Safari Books)
Paul Gries, Jennifer Campbell, Jason Montojo. Practical Programming: An Introduction to Computer Science Using Python 3. Pragmatic Bookshelf, 2013. (Safari Books)

Kurt W. Smith. Cython. O'Reilly, 2015. (Safari Books)
Micha Gorelick, Ian Ozsvald. High Performance Python. O'Reilly, 2014. (Safari Books)
Fernando Doglio, Mastering Python High Performance. Packt Publishing, 2015. (Safari Books)