Numerical Solution of Nonlinear Advection Equation Using Reproducing Kernel Method

Onur Saldır

doi:10.33187/jmsm.1595276

EN

Numerical Solution of Nonlinear Advection Equation Using Reproducing Kernel Method

Abstract

In this study, an iterative approximation is proposed by using the reproducing kernel method (RKM) for the nonlinear advection equation. To apply the iterative RKM, specific reproducing kernel spaces are defined and their kernel functions are presented. The proposed method requires homogenising the initial or boundary conditions of the problem under consideration. After homogenising the initial condition of the advection equation, a linear operator selection is made, and then the approximate solution is constructed using orthonormal basis functions in serial form. Convergence analysis of the approximate solution is demonstrated through the lemma and theorem. Numerical outcomes are provided in the form of graphics and tables to show the efficiency and accuracy of the presented method.

Keywords

Advection equation, Convergence, Iterative solution, Numerical solution, Reproducing kernel method

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Details

Primary Language

English

Subjects

Applied Mathematics (Other)

Journal Section

Research Article

Authors

Onur Saldır ^*
0000-0002-5292-9458
Türkiye

Early Pub Date

December 31, 2024

Publication Date

December 31, 2024

Submission Date

December 2, 2024

Acceptance Date

December 31, 2024

Published in Issue

Year 2024 Volume: 7 Number: 3

DOI

https://doi.org/10.33187/jmsm.1595276

IZ

https://izlik.org/JA67WU93KZ

APA

Saldır, O. (2024). Numerical Solution of Nonlinear Advection Equation Using Reproducing Kernel Method. Journal of Mathematical Sciences and Modelling, 7(3), 157-167. https://doi.org/10.33187/jmsm.1595276

AMA

1.Saldır O. Numerical Solution of Nonlinear Advection Equation Using Reproducing Kernel Method. Journal of Mathematical Sciences and Modelling. 2024;7(3):157-167. doi:10.33187/jmsm.1595276

Chicago

Saldır, Onur. 2024. “Numerical Solution of Nonlinear Advection Equation Using Reproducing Kernel Method”. Journal of Mathematical Sciences and Modelling 7 (3): 157-67. https://doi.org/10.33187/jmsm.1595276.

EndNote

Saldır O (December 1, 2024) Numerical Solution of Nonlinear Advection Equation Using Reproducing Kernel Method. Journal of Mathematical Sciences and Modelling 7 3 157–167.

IEEE

[1]O. Saldır, “Numerical Solution of Nonlinear Advection Equation Using Reproducing Kernel Method”, Journal of Mathematical Sciences and Modelling, vol. 7, no. 3, pp. 157–167, Dec. 2024, doi: 10.33187/jmsm.1595276.

ISNAD

Saldır, Onur. “Numerical Solution of Nonlinear Advection Equation Using Reproducing Kernel Method”. Journal of Mathematical Sciences and Modelling 7/3 (December 1, 2024): 157-167. https://doi.org/10.33187/jmsm.1595276.

JAMA

1.Saldır O. Numerical Solution of Nonlinear Advection Equation Using Reproducing Kernel Method. Journal of Mathematical Sciences and Modelling. 2024;7:157–167.

MLA

Saldır, Onur. “Numerical Solution of Nonlinear Advection Equation Using Reproducing Kernel Method”. Journal of Mathematical Sciences and Modelling, vol. 7, no. 3, Dec. 2024, pp. 157-6, doi:10.33187/jmsm.1595276.

Vancouver

1.Onur Saldır. Numerical Solution of Nonlinear Advection Equation Using Reproducing Kernel Method. Journal of Mathematical Sciences and Modelling. 2024 Dec. 1;7(3):157-6. doi:10.33187/jmsm.1595276