ENHANCING SOLUTIONS FOR NON-LINEAR ORDINARY DIFFERENTIAL EQUATIONS VIA COMBINED LAPLACE TRANSFORM AND REPRODUCING KERNEL METHOD

Ali Akgül; Nourhane Attia

doi:10.11948/20240078

2025 Volume 15 Issue 1

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Article navigation > Journal of Applied Analysis & Computation > 2025 > 15(1): 226-244

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Ali Akgül, Nourhane Attia. ENHANCING SOLUTIONS FOR NON-LINEAR ORDINARY DIFFERENTIAL EQUATIONS VIA COMBINED LAPLACE TRANSFORM AND REPRODUCING KERNEL METHOD[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 226-244. doi: 10.11948/20240078

Citation:

Ali Akgül, Nourhane Attia. ENHANCING SOLUTIONS FOR NON-LINEAR ORDINARY DIFFERENTIAL EQUATIONS VIA COMBINED LAPLACE TRANSFORM AND REPRODUCING KERNEL METHOD[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 226-244. doi: 10.11948/20240078

ENHANCING SOLUTIONS FOR NON-LINEAR ORDINARY DIFFERENTIAL EQUATIONS VIA COMBINED LAPLACE TRANSFORM AND REPRODUCING KERNEL METHOD

Ali Akgül^1,2,,
Nourhane Attia^3, ,

1.
Siirt University, Art and Science Faculty, Department of Mathematics, 56100 Siirt, Turkey
2.
Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
3.
National High School for Marine Sciences and Coastal (ENSSMAL), Dely Ibrahim University Campus, Bois des Cars, B.P. 19, 16320, Algiers, Algeria

Author Bio: Email: ali.akgul@lau.edu.lb(A. Akgül)
Corresponding author: Email: nourhane.attia@enssmal.edu.dz(N. Attia)

Abstract

Abstract

Ordinary differential equations (ODEs) describe diverse phenomena in engineering and physics, such as electrical networks, oscillating systems, satellite orbits, and chemical reactions. Solving these equations, particularly the non-linear ones, is often challenging due to their complexity. This study aims to innovate by integrating the Laplace transform with the reproducing kernel Hilbert space method (RKHSM), introducing an enhanced approach that surpasses classical RKHSM. The combined Laplace-RKHSM method simplifies the original non-linear ODEs, allowing for the construction of novel numerical solutions. These solutions are systematically obtained in series form, providing both analytic and approximate results. The effectiveness and efficacy of the Laplace-RKHSM are demonstrated through three applications, each showcasing the method's superior performance in terms of accuracy and computational efficiency. This new approach not only enhances the existing RKHSM but also broadens its applicability to a wider range of non-linear problems in physics and engineering.
- Reproducing kernel method /
- Laplace transformation /
- non-linear ODEs /
- numerical approximation
MSC: 46E22, 34A08

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References

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