Benedict Leimkuhler has worked extensively for more than two decades on the study of molecular dynamics algorithms. He is the author of research publications on constrained molecular dynamics, temperature controls, stochastic molecular dynamics methods, quantum methods, and advanced integration strategies (multiple time-stepping, adaptive methods). He currently holds the Chair of Applied Mathematics at the University of Edinburgh, is a Fellow of the Royal Society of Edinburgh and a Fellow of the Institute of Mathematics and Its Applications, and is on the editorial boards of four journals.

Charles Matthews obtained his PhD in applied mathematics from the University of Edinburgh, working in the area of numerical methods for stochastic differential equations. He has published research in both chemical physics and mathematics journals on discretization problems in molecular dynamics. He currently is a research staff member in the Department of Statistics at the University of Chicago, investigating sampling methodologies for molecular simulation and the modelling of power networks.

Describes the mathematical underpinnings of algorithms used for molecular dynamics simulation, including both deterministic and stochastic numerical methods

Provides precise statements regarding different numerical procedures which enables selection of the best method for a given problem

Although it is aimed at a broad audience and presumes only basic mathematical preparation, the book presents the relevant theory of Hamiltonian mechanics and stochastic differential equations

Coverage is provided of symplectic numerical methods, constraints and rigid bodies, Langevin dynamics, thermostats and barostats, multiple time-stepping, and the dissipative particle dynamics method

Includes supplementary material: [...]

1.Introduction.- 2.Numerical Integrators.- 3.Analyzing Geometric Integrators.- [...] Stability Threshold.- [...] Space Distributions and Microcanonical Averages.- 6. The Canonical Distribution and Stochastic Differential Equations.- 7. Numerical Methods for Stochastic Molecular Dynamics.- 8. Extended Variable Methods.- References.- Index.