NUMERICAL METHOD FOR SOLVING PSEUDO-HYPERBOLIC EQUATIONS WITH PURELY INTEGRAL CONDITIONS IN REPRODUCING KERNEL HILBERT SPACE

Hadjer Zerouali; Ahcene Merad; Ali Akgül; Douha Saadi; Nourhane Attia; Evren Hincal

doi:10.11948/20240340

2025 Volume 15 Issue 5

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Hadjer Zerouali, Ahcene Merad, Ali Akgül, Douha Saadi, Nourhane Attia, Evren Hincal. NUMERICAL METHOD FOR SOLVING PSEUDO-HYPERBOLIC EQUATIONS WITH PURELY INTEGRAL CONDITIONS IN REPRODUCING KERNEL HILBERT SPACE[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 2611-2636. doi: 10.11948/20240340

Citation:

Hadjer Zerouali, Ahcene Merad, Ali Akgül, Douha Saadi, Nourhane Attia, Evren Hincal. NUMERICAL METHOD FOR SOLVING PSEUDO-HYPERBOLIC EQUATIONS WITH PURELY INTEGRAL CONDITIONS IN REPRODUCING KERNEL HILBERT SPACE[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 2611-2636. doi: 10.11948/20240340

NUMERICAL METHOD FOR SOLVING PSEUDO-HYPERBOLIC EQUATIONS WITH PURELY INTEGRAL CONDITIONS IN REPRODUCING KERNEL HILBERT SPACE

1.
Laboratory of Dynamical Systems and Control, Department of Mathematics and Computer Science, University of Oum El Bouaghi, Oum El Bouaghi 04000, Algeria
2.
Department of Electronics and Communication Engineering, Saveetha School of Engineering, SIMATS, Chennai, Tamilnadu, India
3.
Siirt University, Art and Science Faculty, Department of Mathematics, 56100 Siirt, Turkey
4.
Department of Computer Engineering, Biruni University, 34010 Topkapı, Istanbul, Turkey
5.
Near East University, Mathematics Research Center, Department of Mathematics, Near East Boulevard, PC: 99138, Nicosia/Mersin 10, Turkey
6.
National High School for Marine Sciences and Coastal (ENSSMAL), Dely Ibrahim University Campus, Bois des Cars, B.P. 19, 16320 Algiers, Algeria
7.
Near East University, Department of Mathematics, Mersin 10, TRNC, Turkey
8.
Research Center of Applied Mathematics, Khazar University, Baku, Azerbaijan

Author Bio: Email: hadjer.zerouali@univ-oeb.dz(H. Zerouali); Email: ahcene.merad@univ-oeb.dz(A. Merad); Email: aliakgul00727@gmail.com(A. Akgül); Email: douha.saadi@univ-oeb.dz(D. Saadi); Email: evren.hincal@neu.edu.tr(E. Hincal)
Corresponding author: Email: nourhane.attia@enssmal.edu.dz(N. Attia)

Abstract

Abstract

This paper studies a pseudo-hyperbolic equation with purely integral conditions using the reproducing kernel Hilbert space method (RKHSM). By leveraging the properties of reproducing kernel functions (RKFs), we derive exact and approximate solutions to the equation. We present three numerical examples to assess our approach's efficiency and accuracy. The results demonstrate that the RKHSM yields highly accurate approximations, underscoring its effectiveness as a reliable method for solving pseudo-hyperbolic equations with integral constraints. Our findings contribute to the growing research on analytical and numerical techniques for solving such equations.
- Partial differential equations /
- approximate solutions /
- Gram-Schmidt orthogonalization process /
- computational techniques
MSC: 46E22, 65Nxx

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