Integration of ordinary differential equation with a small parameter via approximate symmetries: Reduction of approximate symmetry algebra to a canonical form
Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences2010 (English)In: Lobachevskii Journal of Mathematics, ISSN 1995-0802, Vol. 31, no 2, 141-151 p.Article in journal (Refereed) Published
Method of integration of second-order ordinary differential equations with twodimensional Lie symmetry algebras by reducing basic symmetries to canonical forms is extended to second-order equations with a small parameter for their approximate integration using two essential approximate symmetries. Canonical forms of basic operators of corresponding approximate Lie algebras Lr, r = 2, 3, 4, as well as general forms of invariant differential equations and their solutions are presented. The similar problems are also solved for systems of two first-order ordinary differential equations with two approximate symmetries.
Place, publisher, year, edition, pages
Pleiades Publishing , 2010. Vol. 31, no 2, 141-151 p.
Integration of ordinary differential equations, Lie symmetry algebras, Ordinary differential equations with a small parameter
IdentifiersURN: urn:nbn:se:bth-7767DOI: 10.1134/S1995080210020058Local ID: oai:bth.se:forskinfoF3007B8E2D71D093C1257758004D7339OAI: oai:DiVA.org:bth-7767DiVA: diva2:835429