New approach to classify second order linear delay differential equations with constant coefficients to solvable Lie algebra

Abstract

The quest of developing efficient and accurate classification scheme for solving second order differential equations (DE) with various coefficients to solvable Lie algebra is never ending. We report a novel classification scheme for second order linear delay differential equations (DDEs) of retarded type with constant coefficients to solvable Lie algebra. The absence of an equivalent transformation related with the change in variables is considered to determine the invariant of DDEs in solvable Lie algebra. The infinitesimal generator of DDEs is used to determine the associated symmetry group. The equations are solved and the solvable Lie algebras spanned by these parameters are obtained by satisfying the inclusion property. This method is further extended to classify neutral delay DE and all classes of second order linear DDEs

Direct Multistep Method for Solving Retarded and Neutral Delay Differential Equation with Boundary and Initial Value Problems

“…The findings confirmed the effectiveness of analytical approaches for resolving NDDE. Analytical techniques such as Lie group analysis to find the exact solutions of second order NDDE has been studied by [15] where they completed the classification of second order non-linear NDDE to solvable Lie algebra. Finally, the convergence of solutions for NDDE is proven by [22] where an example is discussed to illustrate the efficiency of the result.…”