Structure-Preserving Algorithms for Oscillatory Differential by Xinyuan Wu, Xiong You, Bin Wang

By Xinyuan Wu, Xiong You, Bin Wang

Structure-Preserving Algorithms for Oscillatory Differential Equations describes various powerful and effective structure-preserving algorithms for second-order oscillatory differential equations through the use of theoretical research and numerical validation. Structure-preserving algorithms for differential equations, in particular for oscillatory differential equations, play a tremendous position within the exact simulation of oscillatory difficulties in technologies and engineering. The ebook discusses novel advances within the ARKN, ERKN, two-step ERKN, Falkner-type and energy-preserving tools, and so on. for oscillatory differential equations. The paintings is meant for scientists, engineers, academics and scholars who're attracted to structure-preserving algorithms for differential equations. Xinyuan Wu is a professor at Nanjing collage; Xiong You is an affiliate professor at Nanjing Agricultural collage; Bin Wang is a joint Ph.D pupil of Nanjing college and college of Cambridge.

Show description

Read Online or Download Structure-Preserving Algorithms for Oscillatory Differential Equations PDF

Similar algorithms books

A History of Algorithms: From the Pebble to the Microchip

Amazon hyperlink: http://www. amazon. com/History-Algorithms-From-Pebble-Microchip/dp/3540633693

The improvement of computing has reawakened curiosity in algorithms. usually ignored by way of historians and smooth scientists, algorithmic tactics were instrumental within the improvement of basic rules: perform ended in idea simply up to the opposite direction around. the aim of this publication is to supply a historic history to modern algorithmic perform.

Algorithms and Data Structures for External Memory (Foundations and Trends(R) in Theoretical Computer Science)

Information units in huge purposes are frequently too giant to slot thoroughly contained in the computer's inner reminiscence. The ensuing input/output verbal exchange (or I/O) among quick inner reminiscence and slower exterior reminiscence (such as disks) could be a significant functionality bottleneck. Algorithms and knowledge constructions for exterior reminiscence surveys the cutting-edge within the layout and research of exterior reminiscence (or EM) algorithms and information constructions, the place the aim is to use locality and parallelism with a purpose to decrease the I/O bills.

Nonlinear Assignment Problems: Algorithms and Applications

Nonlinear task difficulties (NAPs) are normal extensions of the vintage Linear project challenge, and regardless of the efforts of many researchers during the last 3 many years, they nonetheless stay many of the toughest combinatorial optimization difficulties to unravel precisely. the aim of this e-book is to supply in one quantity, significant algorithmic elements and functions of NAPs as contributed through best overseas specialists.

Algorithms and Computation: 8th International Workshop, WALCOM 2014, Chennai, India, February 13-15, 2014, Proceedings

This ebook constitutes the revised chosen papers of the eighth foreign Workshop on Algorithms and Computation, WALCOM 2014, held in Chennai, India, in February 2014. The 29 complete papers awarded including three invited talks have been rigorously reviewed and chosen from sixty two submissions. The papers are equipped in topical sections on computational geometry, algorithms and approximations, dispensed computing and networks, graph algorithms, complexity and limits, and graph embeddings and drawings.

Extra resources for Structure-Preserving Algorithms for Oscillatory Differential Equations

Sample text

4. 44) p+1 t∈ SN Tq . 3 Dispersion and Dissipation of RK(N) Methods It is known that when the RK(N) methods are used to solve oscillatory differential equations, they usually produce some dispersion and/or dissipation, even though these methods may be of high algebraic orders. 1 RK Methods Let us consider the simplest scalar first-order linear oscillatory equation y = iωy, ω > 0. 45) The true solutions of this equation satisfy y(xn + h) = eiν y(xn ), ν = hω. 46) These solutions are oscillatory with the frequency ω.

32) then become b¯s Mi = bs Ni , bs Ns = b¯s Ms . , φ1 (ν) − cs φ0 (ν) φ0 (ν) + ν 2 ci φ1 (ν) = φ0 (ν) + ν 2 cs φ1 (ν) φ1 (ν) − ci φ0 (ν) , which implies that (ci − cs ) φ02 (ν) + ν 2 φ12 (ν) = 0. From φ02 (ν) + ν 2 φ12 (ν) = 1, it follows that ci = cs , i = 1, . . , s − 1. 18) becomes bi φ0 (ν) + ν 2 Kφ1 (ν) a¯ ij = bj φ0 (ν) + ν 2 Kφ1 (ν) a¯ j i , for i, j = 1, . . , s. Since φ0 (ν) + ν 2 Kφ1 (ν) = 0, we have a¯ j i = i ≤ j. 6 The order of an SARKN method cannot exceed two. 36) i=1 s i=1 40 2 s ARKN Methods b¯i = φ2 (ν) + O(h).

The proof is complete. 38) where K= φ1 (ν) − 12 φ0 (ν) φ0 (ν) + 12 ν 2 φ1 (ν) . 38) is denoted SARKN1s2. 18) and one of the third-order conditions s bi a¯ ij = φ3 (ν) + O(h), i=1 we obtain a one-stage implicit SARKN method of order two: 1/2 1/6 b¯ Kφ1 (ν) b φ1 (ν) where K= φ1 (ν) − 12 φ0 (ν) φ0 (ν) + 12 ν 2 φ1 (ν) . 3 Phase and Stability Properties of Method SARKN1s2 In what follows, we are concerned with the phase and stability properties of the method SARKN1s2. For classical RKN methods, the stability properties are analyzed usually by applying the methods to the second-order homogeneous linear test model q¨ = −λ2 q, λ > 0.

Download PDF sample

Rated 4.81 of 5 – based on 22 votes