A local meshfree method based on radial basis function partition of unity method for two-dimensional (2D) fractional Rayleigh-Stokes problem

Ömer Oruç

doi:10.15672/hujms.1764558

A local meshfree method based on radial basis function partition of unity method for two-dimensional (2D) fractional Rayleigh-Stokes problem

Abstract

This study dedicated to provide numerical solutions of fractional Rayleigh-Stokes problem in two-dimension (2D). The problem has Riemann-Liouville type fractional derivative. To obtain time discretization for the considered problem, we use a difference scheme along with an integration procedure. Hence a time semi-discretized scheme is obtained. We examine stability and convergence of the time semi-discretized scheme. Then we developed a local radial basis function partition of unity method for discretization of space variables. By combining time and space discretization we acquire a full discrete scheme for solving the considered problem. We solve some test problems and compare obtained results for the test problems with existing techniques in the literature, to show efficiency of the proposed method.

Keywords

References

[1] S. Arefian and D. Mirzaei, A compact radial basis function partition of unity method, Comput. Math. Appl. 127, 1-11, 2022

Details

Primary Language

English

Subjects

Numerical Solution of Differential and Integral Equations, Numerical Analysis

Journal Section

Research Article

Authors

Ömer Oruç ^*
0000-0002-6655-3543
Türkiye

Early Pub Date

August 17, 2026

Publication Date

-

Submission Date

August 14, 2025

Acceptance Date

June 5, 2026

Published in Issue

Year 2026 Number: Advanced Online Publication

DOI

https://doi.org/10.15672/hujms.1764558

IZ

https://izlik.org/JA64XB39HL

Cite

RIS / Bibtex

APA

Oruç, Ö. (2026). A local meshfree method based on radial basis function partition of unity method for two-dimensional (2D) fractional Rayleigh-Stokes problem. Hacettepe Journal of Mathematics and Statistics, Advanced Online Publication. https://doi.org/10.15672/hujms.1764558

AMA

1.Oruç Ö. A local meshfree method based on radial basis function partition of unity method for two-dimensional (2D) fractional Rayleigh-Stokes problem. Hacettepe Journal of Mathematics and Statistics. 2026;(Advanced Online Publication). doi:10.15672/hujms.1764558

Chicago

Oruç, Ömer. 2026. “A Local Meshfree Method Based on Radial Basis Function Partition of Unity Method for Two-Dimensional (2D) Fractional Rayleigh-Stokes Problem”. Hacettepe Journal of Mathematics and Statistics, no. Advanced Online Publication. https://doi.org/10.15672/hujms.1764558.

EndNote

Oruç Ö (August 1, 2026) A local meshfree method based on radial basis function partition of unity method for two-dimensional (2D) fractional Rayleigh-Stokes problem. Hacettepe Journal of Mathematics and Statistics Advanced Online Publication

IEEE

[1]Ö. Oruç, “A local meshfree method based on radial basis function partition of unity method for two-dimensional (2D) fractional Rayleigh-Stokes problem”, Hacettepe Journal of Mathematics and Statistics, no. Advanced Online Publication, Aug. 2026, doi: 10.15672/hujms.1764558.

ISNAD

Oruç, Ömer. “A Local Meshfree Method Based on Radial Basis Function Partition of Unity Method for Two-Dimensional (2D) Fractional Rayleigh-Stokes Problem”. Hacettepe Journal of Mathematics and Statistics. Advanced Online Publication (August 1, 2026). https://doi.org/10.15672/hujms.1764558.

JAMA

1.Oruç Ö. A local meshfree method based on radial basis function partition of unity method for two-dimensional (2D) fractional Rayleigh-Stokes problem. Hacettepe Journal of Mathematics and Statistics. 2026. doi:10.15672/hujms.1764558.

MLA

Oruç, Ömer. “A Local Meshfree Method Based on Radial Basis Function Partition of Unity Method for Two-Dimensional (2D) Fractional Rayleigh-Stokes Problem”. Hacettepe Journal of Mathematics and Statistics, no. Advanced Online Publication, Aug. 2026, doi:10.15672/hujms.1764558.

Vancouver

1.Ömer Oruç. A local meshfree method based on radial basis function partition of unity method for two-dimensional (2D) fractional Rayleigh-Stokes problem. Hacettepe Journal of Mathematics and Statistics. 2026 Aug. 1;(Advanced Online Publication). doi:10.15672/hujms.1764558