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Dergiler / Turkish Journal of Mathematics and Computer Science / 2026 / Volume: 18 Issue: 1

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

Nurcan Gücüyenen Kaymak(Doğuş Üniversitesi, İktisadi İdari bilimler Fakültesi, Yönetim bilişim sistemleri)0000-0001-8226-8315
Sayfa
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Yayın Tarihi
2026-02-23
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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.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we present an optimal-order global error analysis for the fully discretized scheme of the Benjamin–Bona–Mahony (BBM) type equations.
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Temel Bulgular & Veri:To support the obtained theoretical results and to demonstrate the effectiveness of the proposed method, four illustrative examples have been studied.
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Sonuç & Katkı: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.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Operator splitting · Fourier collocation · Strang splitting

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.

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Bu Makaleye Atıf Yap

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

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