Approximate solution of integral-algebraic equations of index-2 by numerical multi-step method

bahaa hussein  Alrikabi

doi:10.31642/JoKMC/2018/130105

Authors

bahaa hussein Alrikabi General Directorate of Education in the Holy Karbala Governorate

DOI:

https://doi.org/10.31642/JoKMC/2018/130105

Keywords:

Integral-algebraic equations, Index, Piecewise polynomial numerical method, Convergence analysis

Abstract

This paper presents a numerical approach for solving index-2 integral algebraic equations (IAEs) based on multi-step collocation techniques. The authors first examine the solvability and smoothness of index-2 IAE solutions via the differentiation index framework. The proposed method integrates principles from multi-step methods and collocation, where the approximate solution is determined by satisfying specific matching conditions at designated collocation points. We perform a convergence analysis to prove that the algorithm’s approximations converge to the exact solution and to determine their rate of convergence. For comparison, we also solve the equation using a one-step collocation method, thereby highlighting the superior efficiency and precision of our multi-step approach.

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