Two stage waveform relaxation method for the initial value problems of differential-algebraic equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:236

Article

Bao, Wendi^1,2  Song, Yongzhong¹ 

[1] Nanjing Normal Univ, Sch Math Sci, Inst Math, Jiangsu Key Lab NSLSCS, Nanjing 210046, Jiangsu, Peoples R China

[2] China Univ Petr, Sch Math & Computat Sci, Qingdao 266555, Peoples R China

关键词: Waveform relaxation method;    Differential-algebraic equations (DAEs);    Theta method;    P-regular splitting;    Comparison;   

DOI  :  10.1016/j.cam.2011.07.034

来源: Elsevier

【 摘 要 】

In this paper, we consider a two stage strategy for waveform relaxation (WR) iterations, applied to initial value problems for differential-algebraic equations (DAEs) in the form Ay(t) + By(t) = f(t). Outer iterations of TSWR are defined by M(A)y((k+1)) (t) + M(1)y((k+1)) (t) = N(1)y((k)) (t) + N(A)y((k)) (t) + f(t), where A = M-A - N-A, B = M-1 - N-1, and each iteration y((k+1)) (t) is computed using an inner iterative process, based on another splitting M-1 = M-2 - N-2. Meanwhile, by the means of the Theta method, the discretized TSWR of DAEs is realized. Furthermore, when MA is an Hermitian positive semi-definite matrix with P-regular splittings, the convergence and the comparison theorems of TSWR are analyzed. Finally, the numerical experiments are presented. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

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