Numerical solutions and conservation laws for nonlinear evolution equations.
This paper presents numerical solutions of nonlinear evolution equations using a hybrid collocation method. Nonlinear evolution equations, including the regularized long wave (RLW) equation and the modified regularized long wave (MRLW) equation, play a crucial role in modeling various physical pheno...
| Publicado en: | Zeitschrift für Naturforschung Section A: A Journal of Physical Sciences Vol. 80; no. 1; pp. 9 - 36 |
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| Autores principales: | , |
| Formato: | Artículo |
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De Gruyter
Jan2025
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=182161000&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 182161000 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 09320784 FL07 jtl: Zeitschrift für Naturforschung Section A: A Journal of Physical Sciences issn: 09320784 maglogo: N pubinfo: dt: Jan2025 vid: 80 iid: 1 pid: 1734 pub: De Gruyter artinfo: ui: 182161000 10.1515/zna-2024-0148 ppf: 9 ppct: 27 formats: tig: atl: Numerical solutions and conservation laws for nonlinear evolution equations. aug: au: Anisha Rohila, Rajni affil: Department of Applied Sciences, The Northcap University, Gurugram, India su: Nonlinear evolution equations Nonlinear differential equations Partial differential equations Finite difference method Fourier analysis sug: subj: Nonlinear evolution equations Nonlinear differential equations Partial differential equations Finite difference method Fourier analysis keyword: cubic B-spline functions finite-difference method MRLW and RLW equations stability analysis ab: This paper presents numerical solutions of nonlinear evolution equations using a hybrid collocation method. Nonlinear evolution equations, including the regularized long wave (RLW) equation and the modified regularized long wave (MRLW) equation, play a crucial role in modeling various physical phenomena. A hybrid collocation technique is used for estimating and examining the characteristics of the solitary waves, including their shape, structure, and propagation. The Crank–Nicolson method is used for time discretization and the hybrid collocation method for space discretization. The Fourier series analysis has been used to analyze the stability of the proposed method, and it is established that the hybrid collocation method is unconditionally stable. The accuracy of the proposed scheme is checked by computing the error norm L and the three invariants. The novelty of the method lies in deriving new approximations for the second derivative and applying it on time-dependent nonlinear partial differential equations. A comparison with existing techniques in the literature is conducted to check the improvements in results. The numerical outcomes show that the proposed scheme effectively depicts the conservation laws of solitary waves. The values of three invariants at different time levels have been shown to coincide with their analytical values. The propagation of one, two, and three solitary waves, development of the Maxwellian initial condition into one, two, and more solitary waves, and wave undulations have been illustrated graphically. The method captures the collisions between solitary waves very accurately. Our findings demonstrate that the new cubic B-spline approach offers an accurate and effective solution for the nonlinear evolution equations. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y dt: @attributes: year: 2025 holdings: @attributes: islocal: N |
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