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AuthorAl-Dweik, Ahmad Y.
AuthorMustafa, M. T.
AuthorAzad, H.
AuthorMahomed, F. M.
Available date2021-03-31T08:18:07Z
Publication Date2016
Publication NameMathematical Methods in the Applied Sciences
ResourceScopus
ISSN1704214
URIhttp://dx.doi.org/10.1002/mma.3544
URIhttp://hdl.handle.net/10576/18046
AbstractA new systematic method to find the relative invariant differentiation operators is developed. We incorporate this new approach with Lie's infinitesimal method to study the general class y′′′ = f(x, y, y′, y′′) under general point equivalence transformations in the generic case.As a result, all third‐order differential invariants, relative and absolute invariant differentiation operators are determined for third‐order ODEs y′′′ = f(x, y, y′, y′′), which are not quadratic in the second‐order derivative. These relative invariant differentiation operators are used to determine the fourth‐order differential invariants and absolute invariant differentiation operators in a degenerate case of interest. As an application, invariant descriptions of all the canonical forms in the complex planewith four infinitesimal symmetries for third‐order ODEs y′′′ = f(x, y, y′, y′′), which are not quadratic in the second‐order derivative, are provided.
Languageen
PublisherJohn Wiley and Sons Ltd
Subjectdifferential invariants
equivalence problem
Lie's infinitesimal method
point transformations
relative and absolute invariant differentiation operators
third-order ODEs
TitleInvariants of third‐order ordinary differential equations y′′′=f(x,y,y′,y′′) via point transformations
TypeArticle
Pagination1043-1059
Issue Number5
Volume Number39
dc.accessType Abstract Only


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