Structure-Preserving Algorithms for Oscillatory Differential Equations

ISBN-13: 9783642445569 / Angielski / Miękka / 2015 / 236 str.

Xinyuan Wu;Xiong You; Huntingto Bin Wang (Marshall University

Opis

Structure-Preserving Algorithms for Oscillatory Differential Equations describes a large number of highly effective and efficient structure-preserving algorithms for second-order oscillatory differential equations by using theoretical analysis and numerical validation. Structure-preserving algorithms for differential equations, especially for oscillatory differential equations, play an important role in the accurate simulation of oscillatory problems in applied sciences and engineering. The book discusses novel advances in the ARKN, ERKN, two-step ERKN, Falkner-type and energy-preserving methods, etc. for oscillatory differential equations.The work is intended for scientists, engineers, teachers and students who are interested in structure-preserving algorithms for differential equations. Xinyuan Wu is a professor at Nanjing University; Xiong You is an associate professor at Nanjing Agricultural University; Bin Wang is a joint Ph.D student of Nanjing University and University of Cambridge.

Recenzje

From the reviews:

"The monograph contains a detailed discussion of the class of numerical integrators for oscillatory problems defined by second-order ordinary differential equations. This work is suitable for researchers as well as for students in the field of numerical analysis." (Roland Pulch, zbMATH, Vol. 1276, 2014)

"In this monograph the authors present structure-preserving ODE-solvers for oscillatory IVPs that arise in a wide range of fields such as astronomy, natural sciences and engineering. ... This book is an excellent reference for practicing scientists and engineers who need in-depth information about structure-preserving integration of oscillatory ODEs." (Martin Hermann, Mathematical Reviews, December, 2013)

Spis treści

Runge-Kutta (-Nyström) Methods for Oscillatory Differential Equations.- ARKN Methods.- ERKN Methods.- Symplectic and Symmetric Multidimensional ERKN Methods.- Two-Step Multidimensional ERKN Methods.- Adapted Falkner-Type Methods.- Energy-Preserving ERKN Methods.- Effective Methods for Highly Oscillatory Second-Order Nonlinear Differential Equations.- Extended Leap-Frog Methods for Hamiltonian Wave Equations.