10.1007/s40096-022-00467-z

An error estimation of a Nyström type method for integral-algebraic equations of index-1

  • Sayed Arsalan Sajjadi1,
  • Hashem Saberi Najafi*1,
  • Hossein Aminikhah2,
  1. Department of Applied Mathematics and Computer Science, Faculty of Mathematical Sciences, University of Guilan, Rasht, IR
  2. Department of Applied Mathematics and Computer Science, Faculty of Mathematical Sciences, University of Guilan, Rasht, IR Center of Excellence for Mathematical Modelling, Optimization and Combinational Computing (MMOCC), University of Guilan, Rasht, IR

Published in Issue 2022-04-17

How to Cite

Sajjadi, S. A., Najafi, H. S., & Aminikhah, H. (2022). An error estimation of a Nyström type method for integral-algebraic equations of index-1. Mathematical Sciences, 17(3 (September 2023). https://doi.org/10.1007/s40096-022-00467-z
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Abstract

Abstract This paper presents a numerical method based on the first kind of Chebyshev polynomials for solving a coupled system of Volterra integral equations of the second and first kind. For sake using the theory of orthogonal Chebyshev polynomials, we use some variable transformations to change the mentioned system into a new system on the interval [-1,1]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[-1, 1]$$\end{document} . The integral-algebraic equations belong to the class of moderately ill-posed problems. The main idea in the numerical method is that we will approximate the product of the kernels and solutions which using this idea, we achieve an accurate algorithm. Due to the presence of the first kind Volterra integral equation, convergence analysis can be challenging. We analyze the convergence of this method by computation of over estimate for errors. Finally, the numerical examples confirm the validity of the convergence analysis.

Keywords

  • Numerical analysis,
  • Integral-algebraic equations,
  • Semi-explicit,
  • Convergence analysis,
  • Index-1

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