Introduction

Kang Feng and Mengzhao Qin ()
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Kang Feng: Institute of Computational Mathematics and Scientific/Engineering Computing
Mengzhao Qin: Institute of Computational Mathematics and Scientific/Engineering Computing

A chapter in Symplectic Geometric Algorithms for Hamiltonian Systems, 2010, pp 1-38 from Springer

Abstract: Abstract The main theme of modern scientific computing is the numerical solution of various differential equations of mathematical physics bearing the names, such as Newton, Euler, Lagrange, Laplace, Navier-Stokes, Maxwell, Boltzmann, Einstein, Schrödinger, Yang-Mills, etc. At the top of the list is the most celebrated Newton’s equation of motion. The historical, theoretical and practical importance of Newton’s equation hardly needs any comment, so is the importance of the numerical solution of such equations. On the other hand, starting from Euler, right down to the present computer age, a great wealth of scientific literature on numerical methods for differential equations has been accumulated, and a great variety of algorithms, software packages and even expert systems has been developed. With the development of the modern mechanics, physics, chemistry, and biology, it is undisputed that almost all physical processes, whether they are classical, quantum, or relativistic, can be represented by an Hamiltonian system. Thus, it is important to solve the Hamiltonian system correctly.

Keywords: Hamiltonian System; Symplectic Structure; Hamiltonian Function; Classical Trajectory; Symplectic Geometry (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-01777-3_1

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DOI: 10.1007/978-3-642-01777-3_1

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