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Volume 18, Issue 6
Collocation Methods for a Class of Integro-Differential Algebraic Equations

Haiyan Zhang & Hui Liang

Int. J. Numer. Anal. Mod., 18 (2021), pp. 758-787.

Published online: 2021-11

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  • Abstract

A class of index-1 integro-differential algebraic equations modeling a hydraulic circuit that feed a combustion process is considered. The existence, uniqueness and regularity are analyzed in detail. Two kinds of collocation methods are employed to solve the equation numerically. For the first one, the derivative and algebraic components are approximated in globally continuous and discontinuous polynomial spaces, respectively; and for another one, both the derivative and algebraic components are solved in globally continuous piecewise polynomial spaces. The convergence, global and local superconvergence are described for these two classes of collocation methods. Some numerical experiments are given to illustrate the obtained theoretical results.

  • Keywords

Integro-differential algebraic equations, tractability index, regularity, collocation methods, convergence analysis.

  • AMS Subject Headings

45J99, 65R99

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-18-758, author = {Zhang , Haiyan and Liang , Hui}, title = {Collocation Methods for a Class of Integro-Differential Algebraic Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2021}, volume = {18}, number = {6}, pages = {758--787}, abstract = {

A class of index-1 integro-differential algebraic equations modeling a hydraulic circuit that feed a combustion process is considered. The existence, uniqueness and regularity are analyzed in detail. Two kinds of collocation methods are employed to solve the equation numerically. For the first one, the derivative and algebraic components are approximated in globally continuous and discontinuous polynomial spaces, respectively; and for another one, both the derivative and algebraic components are solved in globally continuous piecewise polynomial spaces. The convergence, global and local superconvergence are described for these two classes of collocation methods. Some numerical experiments are given to illustrate the obtained theoretical results.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/19949.html} }
TY - JOUR T1 - Collocation Methods for a Class of Integro-Differential Algebraic Equations AU - Zhang , Haiyan AU - Liang , Hui JO - International Journal of Numerical Analysis and Modeling VL - 6 SP - 758 EP - 787 PY - 2021 DA - 2021/11 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/19949.html KW - Integro-differential algebraic equations, tractability index, regularity, collocation methods, convergence analysis. AB -

A class of index-1 integro-differential algebraic equations modeling a hydraulic circuit that feed a combustion process is considered. The existence, uniqueness and regularity are analyzed in detail. Two kinds of collocation methods are employed to solve the equation numerically. For the first one, the derivative and algebraic components are approximated in globally continuous and discontinuous polynomial spaces, respectively; and for another one, both the derivative and algebraic components are solved in globally continuous piecewise polynomial spaces. The convergence, global and local superconvergence are described for these two classes of collocation methods. Some numerical experiments are given to illustrate the obtained theoretical results.

Zhang , Haiyan and Liang , Hui. (2021). Collocation Methods for a Class of Integro-Differential Algebraic Equations. International Journal of Numerical Analysis and Modeling. 18 (6). 758-787. doi:
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