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Structure-Preserving Algorithms for Oscillatory Differential Equations de Xinyuan Wu

Structure-Preserving Algorithms for Oscillatory Differential Equations

Autor Xinyuan Wu, Xiong You, Bin Wang
en Limba Engleză Hardback – 2 feb 2013
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.
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Specificații

ISBN-13: 9783642353376
ISBN-10: 3642353371
Pagini: 252
Ilustrații: XII, 236 p. 40 illus., 2 illus. in color.
Dimensiuni: 160 x 241 x 19 mm
Greutate: 0.5 kg
Ediția:2013
Editura: Springer
Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Cuprins

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.

Recenzii

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)

Textul de pe ultima copertă

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.

Caracteristici

Includes recent advances in the ARKN methods, ERKN methods, two-step ERKN methods, energy-preserving methods, etc.
Focuses on new and important development of rooted-tree and B-series theories with applications in derivation of order conditions for new RKN-type methods
Places emphasis on the structure-preserving properties and computational efficiency of newly developed integrators
Includes supplementary material: sn.pub/extras

Notă biografică

Xinyuan Wu, a Professor in Department of Mathematics, Nanjing University. His research interests focus on geometric algorithms for differential equations, numerical methods for stiff problems and numerical methods for algebraic systems. ¿In 2017, Wu was awarded with the highest distinction of "Honorary Fellowship" from European Society of Computational Methods in Science and Engineering for the outstanding contribution in the fields of Numerical Analysis and Applied Mathematics. Wu attended the school of Mathematics at the University of Tübingen for study and research from Janurary 19th 2002 to Janurary 20th 2003.
Bin Wang, a Professor in Department of Mathematics and Statistics, Xi'an Jiaotong University. His research interests focus on various structure-preserving algorithms as well as numerical methods for differential equation, especially the numerical computation and analysis of Hamilton ordinary differential equation and partial differential equation. Wang was awarded by Alexander von Humboldt Foundation (2017-2019).