Volume 32, Issue 6
On Solvability and Waveform Relaxation Methods of Linear Variable-Coefficient Differential-Algebraic Equations

Xi Yang

J. Comp. Math., 32 (2014), pp. 696-720

Published online: 2014-12

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  • Abstract

This paper is concerned with the solvability and waveform relaxation methods of linear variable-coefficient differential-algebraic equations (DAEs). Most of the previous works have been focused on linear variable-coefficient DAEs with smooth coefficients and data, yet no results related to the convergence rate of the corresponding waveform relaxation methods has been obtained. In this paper, we develope the solvability theory for the linear variable-coefficient DAEs on Legesgue square-integrable function space in both traditional and least squares senses, and determine the convergence rate of the waveform relaxation methods for solving linear variable-coefficient DAEs.

  • Keywords

Differential-algebraic equations Integral operator Fourier transform Waveform relaxation method

  • AMS Subject Headings

65F10 65L20 65L80 65R10 65R20.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-32-696, author = {Xi Yang}, title = {On Solvability and Waveform Relaxation Methods of Linear Variable-Coefficient Differential-Algebraic Equations}, journal = {Journal of Computational Mathematics}, year = {2014}, volume = {32}, number = {6}, pages = {696--720}, abstract = { This paper is concerned with the solvability and waveform relaxation methods of linear variable-coefficient differential-algebraic equations (DAEs). Most of the previous works have been focused on linear variable-coefficient DAEs with smooth coefficients and data, yet no results related to the convergence rate of the corresponding waveform relaxation methods has been obtained. In this paper, we develope the solvability theory for the linear variable-coefficient DAEs on Legesgue square-integrable function space in both traditional and least squares senses, and determine the convergence rate of the waveform relaxation methods for solving linear variable-coefficient DAEs.}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1405-m4417}, url = {http://global-sci.org/intro/article_detail/jcm/8410.html} }
TY - JOUR T1 - On Solvability and Waveform Relaxation Methods of Linear Variable-Coefficient Differential-Algebraic Equations AU - Xi Yang JO - Journal of Computational Mathematics VL - 6 SP - 696 EP - 720 PY - 2014 DA - 2014/12 SN - 32 DO - http://doi.org/10.4208/jcm.1405-m4417 UR - https://global-sci.org/intro/article_detail/jcm/8410.html KW - Differential-algebraic equations KW - Integral operator KW - Fourier transform KW - Waveform relaxation method AB - This paper is concerned with the solvability and waveform relaxation methods of linear variable-coefficient differential-algebraic equations (DAEs). Most of the previous works have been focused on linear variable-coefficient DAEs with smooth coefficients and data, yet no results related to the convergence rate of the corresponding waveform relaxation methods has been obtained. In this paper, we develope the solvability theory for the linear variable-coefficient DAEs on Legesgue square-integrable function space in both traditional and least squares senses, and determine the convergence rate of the waveform relaxation methods for solving linear variable-coefficient DAEs.
Xi Yang. (1970). On Solvability and Waveform Relaxation Methods of Linear Variable-Coefficient Differential-Algebraic Equations. Journal of Computational Mathematics. 32 (6). 696-720. doi:10.4208/jcm.1405-m4417
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