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

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 mentione...

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Veröffentlicht in:Mathematical sciences (Karaj, Iran) Jg. 17; H. 3; S. 253 - 265
Hauptverfasser: Sajjadi, Sayed Arsalan, Najafi, Hashem Saberi, Aminikhah, Hossein
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2023
Springer Nature B.V
Schlagworte:
Algebra
Algorithms
Applications of Mathematics
Applied mathematics
Chebyshev approximation
Convergence
Growth models
Ill posed problems
Inequality
Integral equations
Mathematical functions
Mathematics
Mathematics and Statistics
Numerical analysis
Numerical methods
Original Research
Polynomials
Volterra integral equations
45Fxx
Numerical analysis
Integral-algebraic equations
Index-1
45D05
Semi-explicit
Convergence analysis
ISSN:2008-1359, 2251-7456
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Zusammenfassung: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 ] . 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.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2008-1359
2251-7456
DOI:10.1007/s40096-022-00467-z