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Dear authors! Submission of all materials is carried out only electronically through Online Submission System in personal account. DOI: 10.46698/z4764-9590-5591-k Quadrature Formula of the Highest Algebraic Degree of Accuracy Containing Predefined Nods
Khubezhty, Sh. S.
Vladikavkaz Mathematical Journal 2023. Vol. 25. Issue 1.
Abstract:
Approximate methods for calculating definite integrals are relevant to this day. Among them, the quadrature methods are the most popular as they enables one to calculate approximately the integral using a finite number of values of the integrable function. In addition, in many cases, less computational labor is required compared to other methods. Using Chebyshev polynomials of the first, second, third, and fourth kind corresponding to the weight functions \(p(x)=\frac{1}{\sqrt{1-x^2}}\), \(p(x)=\sqrt{1- x^2}\), \(p(x)=\sqrt{\frac{1+x}{1-x}}\), \(p(x)=\sqrt{\frac{1-x}{1+x }}\), on the segment \([-1,1]\), quadrature formulas are constructed with predefined nodes \(a_1=-1\), \(a_2=1\), and estimates of the remainder terms with degrees of accuracy \(2n+1\). In this case, a special place is occupied by the construction of orthogonal polynomials with respect to the weight \(p(x)(x^2-1)\) and finding their roots. This problem turned out to be laborious and was solved by methods of computational mathematics.
Keywords: weight functions, orthogonal polynomials, quadrature formulas, predetermined nodes, remainder terms, degrees of accuracy
Language: Russian
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 For citation: Khubezhty, Sh. S. Quadrature Formula of the Highest Algebraic Degree of Accuracy Containing Predefined Nods, Vladikavkaz Math. J., 2023, vol. 25, no. 1, pp.131-140 (in Russian).
DOI 10.46698/z4764-9590-5591-k ← Contents of issue |
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