Some new super convergence of a quartic integro-spline at the mid-knots of a uniform partition

Lang, Feng-Gong; Xu, Xiaoping

doi:10.2306/scienceasia1513-1874.2022.063

Cited by 3 publications

(3 citation statements)

References 17 publications

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“…To construct an integro-spline, we generally need n integral values I j ( j = 0, 1, • • •, n − 1) and several boundary conditions. In recent years, there are many studies about integro-spline interpolation ( [1,2,3,4,5,6,7,8,9,10,11,12]).…”

Section: The Authors and Ios Press This Article Is Published Online W...mentioning

confidence: 99%

“…In [12], the authors derived the approximation properties of the aforementioned two kinds of quartic integro-splines at the mid-knots. Specifically, the two quartic integrosplines exhibit superconvergence (sixth-order, fourth-order and second-order, respectively) in approximating function values, second-order derivative values and fourthorder derivative values at the mid-knots.…”

Section: The Authors and Ios Press This Article Is Published Online W...mentioning

confidence: 99%

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On a New Kind of Quartic Integro-Spline Over a Uniform Partition

Lang,

Zhang

2023

Fuzzy Systems and Data Mining IX

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In this paper, we construct a new kind of quartic integro-spline by applying two constraints on integral values to the piecewise polynomials on the first and the last subintervals, respectively. This quartic integro-spline does not require any additional given boundary values and is relatively simple to implement. It is theoretically proved that this integro-spline has a satisfactory convergence rate for approximating unknown functions and its derivatives at the knots. Especially for an unknown function y with fifth order derivative values of 0 at the left and right endpoints, its approximation of function values and second-order derivative values may even exhibit superconvergence at the knots. Numerical experiments have verified our theoretical results and compared the differences in approximation performance between our quartic integro-spline and other integro-splines.

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Section: The Authors and Ios Press This Article Is Published Online W...mentioning

confidence: 99%

Section: The Authors and Ios Press This Article Is Published Online W...mentioning

confidence: 99%

On a New Kind of Quartic Integro-Spline Over a Uniform Partition

Lang,

Zhang

2023

Fuzzy Systems and Data Mining IX

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“…To enhance these algorithms, the concept of quadratic uniform B-spline was explored in [13,14]. Furthermore, the study of integro splines quasi-interpolants and their super convergence properties is documented in [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Cutting-Edge Computational Approaches for Approximating Nonlocal Variable-Order Operators

Tanha,

Parsa Moghaddam,

Ilie

2024

Computation

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This study presents an algorithmically efficient approach to address the complexities associated with nonlocal variable-order operators characterized by diverse definitions. The proposed method employs integro spline quasi interpolation to approximate these operators, aiming for enhanced accuracy and computational efficiency. We conduct a thorough comparison of the outcomes obtained through this approach with other established techniques, including finite difference, IQS, and B-spline methods, documented in the applied mathematics literature for handling nonlocal variable-order derivatives and integrals. The numerical results, showcased in this paper, serve as a compelling validation of the notable advantages offered by our innovative approach. Furthermore, this study delves into the impact of selecting different variable-order values, contributing to a deeper understanding of the algorithm’s behavior across a spectrum of scenarios. In summary, this research seeks to provide a practical and effective solution to the challenges associated with nonlocal variable-order operators, contributing to the applied mathematics literature.

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