Convergence analysis of piecewise continuous collocation methods for higher index integral algebraic equations of the Hessenberg type

Babak Shiri; Sedaghat Shahmorad; Gholamreza Hojjati

International Journal of Applied Mathematics and Computer Science (2013)

  • Volume: 23, Issue: 2, page 341-355
  • ISSN: 1641-876X

Abstract

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In this paper, we deal with a system of integral algebraic equations of the Hessenberg type. Using a new index definition, the existence and uniqueness of a solution to this system are studied. The well-known piecewise continuous collocation methods are used to solve this system numerically, and the convergence properties of the perturbed piecewise continuous collocation methods are investigated to obtain the order of convergence for the given numerical methods. Finally, some numerical experiments are provided to support the theoretical results.

How to cite

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Babak Shiri, Sedaghat Shahmorad, and Gholamreza Hojjati. "Convergence analysis of piecewise continuous collocation methods for higher index integral algebraic equations of the Hessenberg type." International Journal of Applied Mathematics and Computer Science 23.2 (2013): 341-355. <http://eudml.org/doc/256713>.

@article{BabakShiri2013,
abstract = {In this paper, we deal with a system of integral algebraic equations of the Hessenberg type. Using a new index definition, the existence and uniqueness of a solution to this system are studied. The well-known piecewise continuous collocation methods are used to solve this system numerically, and the convergence properties of the perturbed piecewise continuous collocation methods are investigated to obtain the order of convergence for the given numerical methods. Finally, some numerical experiments are provided to support the theoretical results.},
author = {Babak Shiri, Sedaghat Shahmorad, Gholamreza Hojjati},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {piecewise continuous collocations methods; Volterra integral equations; integral algebraic equations; piecewise continuous collocation methods; high index Volterra integral algebraic equations; convergence; system of first kind Volterra linear integral equations; Newton's iterative method; numerical examples},
language = {eng},
number = {2},
pages = {341-355},
title = {Convergence analysis of piecewise continuous collocation methods for higher index integral algebraic equations of the Hessenberg type},
url = {http://eudml.org/doc/256713},
volume = {23},
year = {2013},
}

TY - JOUR
AU - Babak Shiri
AU - Sedaghat Shahmorad
AU - Gholamreza Hojjati
TI - Convergence analysis of piecewise continuous collocation methods for higher index integral algebraic equations of the Hessenberg type
JO - International Journal of Applied Mathematics and Computer Science
PY - 2013
VL - 23
IS - 2
SP - 341
EP - 355
AB - In this paper, we deal with a system of integral algebraic equations of the Hessenberg type. Using a new index definition, the existence and uniqueness of a solution to this system are studied. The well-known piecewise continuous collocation methods are used to solve this system numerically, and the convergence properties of the perturbed piecewise continuous collocation methods are investigated to obtain the order of convergence for the given numerical methods. Finally, some numerical experiments are provided to support the theoretical results.
LA - eng
KW - piecewise continuous collocations methods; Volterra integral equations; integral algebraic equations; piecewise continuous collocation methods; high index Volterra integral algebraic equations; convergence; system of first kind Volterra linear integral equations; Newton's iterative method; numerical examples
UR - http://eudml.org/doc/256713
ER -

References

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