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 - <p style="text-align: justify;">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.</p>