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

Babak Shiri, Sedaghat Shahmorad, Gholamreza Hojjati (2013)

International Journal of Applied Mathematics and Computer Science

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...

Convergence domains under Zabrejko-Zinčenko conditions using recurrent functions

Ioannis K. Argyros, Saïd Hilout (2011)

Applicationes Mathematicae

We provide a semilocal convergence analysis for Newton-type methods using our idea of recurrent functions in a Banach space setting. We use Zabrejko-Zinčenko conditions. In particular, we show that the convergence domains given before can be extended under the same computational cost. Numerical examples are also provided to show that we can solve equations in cases not covered before.

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