Error Estimates of the Fourier Collocation Combined Strang Splitting Method for Benjamin-Bona-Mahony Type Equations

Nurcan Gücüyenen Kaymak

doi:10.47000/tjmcs.1674288

Error Estimates of the Fourier Collocation Combined Strang Splitting Method for Benjamin-Bona-Mahony Type Equations

Abstract

In this paper, we present an optimal-order global error analysis for the fully discretized scheme of the Benjamin–Bona–Mahony (BBM) type equations. The BBM equation is splitted into two parts: linear and nonlinear parts. Then the Strang splitting method is applied in time while the Fourier collocation method is studied for space discretization. Semi-discrete and fully discrete Fourier collocation schemes are constructed. The convergence of the fully discretized scheme is established using the global time discretization error and the Fourier interpolation error, under appropriate regularity assumptions on the exact solution. To support the obtained theoretical results and to demonstrate the effectiveness of the proposed method, four illustrative examples have been studied. In addition, the performance of the method has been examined on a single soliton wave equation, where the corresponding mass, energy and momentum values are presented to show that the scheme is preserved.

Keywords

References

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Details

Primary Language

English

Subjects

Numerical Analysis, Mathematical Methods and Special Functions

Journal Section

Research Article

Authors

Nurcan Gücüyenen Kaymak ^*
0000-0001-8226-8315
Türkiye

Publication Date

February 23, 2026

Submission Date

April 11, 2025

Acceptance Date

November 11, 2025

Published in Issue

Year 2026 Volume: 18 Number: 1

DOI

https://doi.org/10.47000/tjmcs.1674288

IZ

https://izlik.org/JA24ST92BX

Cite

RIS / Bibtex

APA

Gücüyenen Kaymak, N. (2026). Error Estimates of the Fourier Collocation Combined Strang Splitting Method for Benjamin-Bona-Mahony Type Equations. Turkish Journal of Mathematics and Computer Science, 18(1), 78-94. https://doi.org/10.47000/tjmcs.1674288

AMA

1.Gücüyenen Kaymak N. Error Estimates of the Fourier Collocation Combined Strang Splitting Method for Benjamin-Bona-Mahony Type Equations. TJMCS. 2026;18(1):78-94. doi:10.47000/tjmcs.1674288

Chicago

Gücüyenen Kaymak, Nurcan. 2026. “Error Estimates of the Fourier Collocation Combined Strang Splitting Method for Benjamin-Bona-Mahony Type Equations”. Turkish Journal of Mathematics and Computer Science 18 (1): 78-94. https://doi.org/10.47000/tjmcs.1674288.

EndNote

Gücüyenen Kaymak N (February 1, 2026) Error Estimates of the Fourier Collocation Combined Strang Splitting Method for Benjamin-Bona-Mahony Type Equations. Turkish Journal of Mathematics and Computer Science 18 1 78–94.

IEEE

[1]N. Gücüyenen Kaymak, “Error Estimates of the Fourier Collocation Combined Strang Splitting Method for Benjamin-Bona-Mahony Type Equations”, TJMCS, vol. 18, no. 1, pp. 78–94, Feb. 2026, doi: 10.47000/tjmcs.1674288.

ISNAD

Gücüyenen Kaymak, Nurcan. “Error Estimates of the Fourier Collocation Combined Strang Splitting Method for Benjamin-Bona-Mahony Type Equations”. Turkish Journal of Mathematics and Computer Science 18/1 (February 1, 2026): 78-94. https://doi.org/10.47000/tjmcs.1674288.

JAMA

1.Gücüyenen Kaymak N. Error Estimates of the Fourier Collocation Combined Strang Splitting Method for Benjamin-Bona-Mahony Type Equations. TJMCS. 2026;18:78–94.

MLA

Gücüyenen Kaymak, Nurcan. “Error Estimates of the Fourier Collocation Combined Strang Splitting Method for Benjamin-Bona-Mahony Type Equations”. Turkish Journal of Mathematics and Computer Science, vol. 18, no. 1, Feb. 2026, pp. 78-94, doi:10.47000/tjmcs.1674288.

Vancouver

1.Nurcan Gücüyenen Kaymak. Error Estimates of the Fourier Collocation Combined Strang Splitting Method for Benjamin-Bona-Mahony Type Equations. TJMCS. 2026 Feb. 1;18(1):78-94. doi:10.47000/tjmcs.1674288