MDPI - Publisher of Open Access Journals

15 pages, 315 KiB

Open AccessArticle

by Geno Nikolov and Petar Nikolov

Mathematics 2024, 12(23), 3783; https://doi.org/10.3390/math12233783 - 29 Nov 2024

Viewed by 652

We study two modifications of the trapezoidal product cubature formulae, approximating double integrals over the square domain

{[a, b]}^{2} = [a, b] \times [a, b]

. Our modified cubature formulae use mixed type [...] Read more.

We study two modifications of the trapezoidal product cubature formulae, approximating double integrals over the square domain

{[a, b]}^{2} = [a, b] \times [a, b]

. Our modified cubature formulae use mixed type data: except evaluations of the integrand on the points forming a uniform grid on

{[a, b]}^{2}

, they involve two or four univariate integrals. A useful property of these cubature formulae is that they are definite of order

(2, 2)

, that is, they provide one-sided approximation to the double integral for real-valued integrands from the class

C^{2, 2} [a, b] = {f (x, y) : \frac{\partial^{4} f}{\partial x^{2} \partial y^{2}} continuous and does not change sign in {(a, b)}^{2}}

. For integrands from

C^{2, 2} [a, b]

we prove monotonicity of the remainders and derive a posteriori error estimates. Full article

(This article belongs to the Special Issue Approximation Theory and Applications)

Search Results (1)