COMPRESSIVE SPLIT-STEP FOURIER METHOD

BAYINDIR, C.

COMPRESSIVE SPLIT-STEP FOURIER METHOD

C. BAYINDIR (Işık Üniversitesi, İnşaat Mühendisliği Bölümü, İstanbul, Türkiye)

TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics

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Yıl: 2015 Cilt: 5 Sayı: 2 Sayfa Aralığı: 298 - 306 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

COMPRESSIVE SPLIT-STEP FOURIER METHOD

Öz:

In this paper an approach for decreasing the computational effort required for the split-step Fourier method (SSFM) is introduced. It is shown that using the sparsity property of the simulated signals, the compressive sampling algorithm can be used as a very efficient tool for the split-step spectral simulations of various phenomena which can be modeled by using differential equations. The proposed method depends on the idea of using a smaller number of spectral components compared to the classical split-step Fourier method with a high number of components. After performing the time integration with a smaller number of spectral components and using the compressive sampling technique with l1 minimization, it is shown that the sparse signal can be reconstructed with a significantly better efficiency compared to the classical split-step Fourier method. Proposed method can be named as compressive split-step Fourier method (CSSFM). For testing of the proposed method the Nonlinear Schr¨odinger Equation and its one-soliton and two-soliton solutions are considered.

Anahtar Kelime:

Konular: Matematik

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

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APA	BAYINDIR C (2015). COMPRESSIVE SPLIT-STEP FOURIER METHOD. , 298 - 306.
Chicago	BAYINDIR C. COMPRESSIVE SPLIT-STEP FOURIER METHOD. (2015): 298 - 306.
MLA	BAYINDIR C. COMPRESSIVE SPLIT-STEP FOURIER METHOD. , 2015, ss.298 - 306.
AMA	BAYINDIR C COMPRESSIVE SPLIT-STEP FOURIER METHOD. . 2015; 298 - 306.
Vancouver	BAYINDIR C COMPRESSIVE SPLIT-STEP FOURIER METHOD. . 2015; 298 - 306.
IEEE	BAYINDIR C "COMPRESSIVE SPLIT-STEP FOURIER METHOD." , ss.298 - 306, 2015.
ISNAD	BAYINDIR, C.. "COMPRESSIVE SPLIT-STEP FOURIER METHOD". (2015), 298-306.

APA	BAYINDIR C (2015). COMPRESSIVE SPLIT-STEP FOURIER METHOD. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, 5(2), 298 - 306.
Chicago	BAYINDIR C. COMPRESSIVE SPLIT-STEP FOURIER METHOD. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics 5, no.2 (2015): 298 - 306.
MLA	BAYINDIR C. COMPRESSIVE SPLIT-STEP FOURIER METHOD. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, vol.5, no.2, 2015, ss.298 - 306.
AMA	BAYINDIR C COMPRESSIVE SPLIT-STEP FOURIER METHOD. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics. 2015; 5(2): 298 - 306.
Vancouver	BAYINDIR C COMPRESSIVE SPLIT-STEP FOURIER METHOD. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics. 2015; 5(2): 298 - 306.
IEEE	BAYINDIR C "COMPRESSIVE SPLIT-STEP FOURIER METHOD." TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, 5, ss.298 - 306, 2015.
ISNAD	BAYINDIR, C.. "COMPRESSIVE SPLIT-STEP FOURIER METHOD". TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics 5/2 (2015), 298-306.