Lie symmetries of first order neutral differential equations

• Autorzy: Lobo Jervin Zen , Valaulikar Y.S.

Identyfikatory

DOI

10.17512/jamcm.2019.1.03

• Języki publikacji: EN

Abstrakty

EN

In this paper we extend the method of obtaining symmetries of ordinary differential equations to first order non-homogeneous neutral differential equations with variable coefficients. The existing method for delay differential equations uses a Lie-Bäcklund operator and an Invariant Manifold Theorem to define the operators which are used to obtain the infinitesimal generators of the Lie group. In this paper, we adopt a different approach and use Taylor’s theorem to obtain a Lie type invariance condition and the determining equations for a neutral differential equation. We then split this equation in a manner similar to that of ordinary differential equations to obtain an over-determined system of partial differential equations. These equations are then solved to obtain corresponding infinitesimals, and hence desired equivalent symmetries. We then obtain the symmetry algebra admitted by this neutral differential equation.

Słowa kluczowe

EN

determining equations; infinitesimals; invariance; neutral differential equations; splitting equations; symmetries

PL

równanie różniczkowe pierwszego rzędu; warunek niezmienności; symetrie; równanie różniczkowe neutralne

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2019
• Tom: Vol. 18, nr 1
• Strony: 29--40
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Lobo Jervin Zen

• Department of Mathematics, St. Xavier’s College Mapusa, Goa - 403507, India

autor

Valaulikar Y.S.

• Department of Mathematics, Goa University Taleigao Plateau, Goa - 403206, India

Bibliografia

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• [15] Muhsen, L., & Maan, N. (2016). Lie group analysis of second-order non-linear neutral delay differential equations. Malaysian Journal of Mathematical Sciences, 10(S), 117-129.
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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).