GROUP METHODS FOR SECOND ORDER DELAY DIFFERENTIAL EQUATIONS

GROUP METHODS FOR SECOND ORDER DELAY DIFFERENTIAL EQUATIONS

J. Z. Lobo, Y. S. Valaulikar

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Abstract

In this research paper, we obtain the equivalent symmetries of non-homogeneous second order delay dierential equations with variable coecients. Group methods have been used to do this. The approach followed by us to obtain a Lie type invariance condition for the second order delay dierential equation is by using Taylor's theorem for a function of more than one variable. This Lie type invariance condition established by us in this paper, will be used to obtain the determining equations of the second order delay dierential equation. We study certain cases under which the delay dierential equation admits innitesimal generators. Further, by performing symmetry analysis of this delay dierential equation, the complete group classication for it has been made.

Keywords

Delay dierential equation, determining equations, Lie group, Lie invariance condition, splitting equation, symmetries.