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Reproducing kernel method of solving singular integral equation with cosecant kernel [PDF]

Journal of Mathematical Analysis and Applications, 2008
In the paper, a reproducing kernel method of solving singular integral equations (SIE) with cosecant kernel is proposed. For solving SIE, difficulties lie in its singular term. In order to remove singular term of SIE, an equivalent transformation is made.
Jihong Shen
exaly   +2 more sources

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Fitted fractional reproducing kernel algorithm for the numerical solutions of ABC – Fractional Volterra integro-differential equations

Chaos, Solitons & Fractals, 2019
This paper focuses on providing a novel high-order algorithm for the numerical solutions of fractional order Volterra integro-differential equations using Atangana–Baleanu approach by employing the reproducing kernel approximation.
O. Arqub, Banan Maayah
semanticscholar   +1 more source

Numerical simulation of time-fractional partial differential equations arising in fluid flows via reproducing Kernel method

International journal of numerical methods for heat & fluid flow, 2019
Purpose The subject of the fractional calculus theory has gained considerable popularity and importance due to their attractive applications in widespread fields of physics and engineering.
Omar Abu Arqub
semanticscholar   +1 more source

Modulation of reproducing kernel Hilbert space method for numerical solutions of Riccati and Bernoulli equations in the Atangana-Baleanu fractional sense

Chaos, Solitons & Fractals, 2019
This article is concerned with design and comprehensive study of a numerical approach for solving Riccati and Bernoulli equations in the Atangana-Baleanu fractional sense.
Omar Abu Arqub, Banan Maayah
semanticscholar   +1 more source

On Reproducing Kernel Banach Spaces: Generic Definitions and Unified Framework of Constructions

Acta Mathematica Sinica. English series, 2019
Recently, there has been emerging interest in constructing reproducing kernel Banach spaces (RKBS) for applied and theoretical purposes such as machine learning, sampling reconstruction, sparse approximation and functional analysis.
Rongrong Lin, Hai-Zhang Zhang, Jun Zhang
semanticscholar   +1 more source

A stable least residue method in reproducing kernel space for solving a nonlinear fractional integro-differential equation with a weakly singular kernel

, 2020
A stable least residue method for solving a nonlinear fractional integro-differential equation with a weakly singular kernel in the reproducing kernel space is proposed.
Hong Du, Zhong Chen, Tie-Jun Yang
semanticscholar   +1 more source

Numerical solution of functionally graded materials based on radial basis reproducing kernel particle method

, 2020
In this paper, the radial basis function (RBF) is used to construct the approximating function of the reproducing kernel particle method (RKPM), which can eliminate the negative effect of different kernel functions on the calculating accuracy. The radial
Zheng Liu, Gao-Feng Wei, Zhi-Ming Wang
semanticscholar   +1 more source

Reproducing kernel Hilbert spaces

High-Dimensional Statistics, 2019
This chapter introduces an elegant mathematical theory that has been developed for nonparametric regression with penalized estimation.
Ronald Christensen
semanticscholar   +1 more source

Crank–Nicholson difference method and reproducing kernel function for third order fractional differential equations in the sense of Atangana–Baleanu Caputo derivative

Chaos, Solitons & Fractals, 2019
In this paper, the third order partial differential equation defined by Caputo fractional derivative with Atangana–Baleanu derivative has been investigated. The stability estimates are proved for the exact solution. Difference schemes for Crank–Nicholson
A. Akgül, Mahmut Modanlı
semanticscholar   +1 more source

Numerical solutions and geometric attractors of a fractional model of the cancer-immune based on the Atangana-Baleanu-Caputo derivative and the reproducing kernel scheme

Zhongguó wùli xuékan, 2022
Banan Maayah, O. Arqub, S. Alnabulsi, Hamed Alsulami   +3 more
semanticscholar   +1 more source