Abstract
This paper gives sufficient conditions for existence and uniqueness of solutions and for the convergence of Picard iterations and more general waveform relaxation methods for differential-algebraic systems of neutral type. The results are obtained by the contraction mapping principle on Banach spaces with weighted norms and by the use of the Perron-Frobenius theory of nonnegative and nonreducible matrices. It is demonstrated that waveform relaxation methods are convergent faster than the classical Picard iterations.
Original language | English (US) |
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Pages (from-to) | 2303-2317 |
Number of pages | 15 |
Journal | SIAM Journal on Numerical Analysis |
Volume | 33 |
Issue number | 6 |
DOIs | |
State | Published - Dec 1996 |
Keywords
- Differential-algebraic system
- Picard iterations
- Waveform relaxation
ASJC Scopus subject areas
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics