In this work, Galerkin approximations are developed for a system of first order nonlinear neutral delay differential equations (NDDEs). The NDDEs are converted into an equivalent system of hyperbolic partial differential equations (PDEs) along with the nonlinear boundary constraints. Lagrange multipliers are introduced to enforce the boundary constraints. The explicit expressions for the Lagrange multipliers are derived by exploiting the equivalence of partial derivatives in space and time at a given point on the domain. To illustrate the method, comparisons are made between numerical solution of NDDEs and its Galerkin approximations for different NDDEs.
Galerkin Approximations for Neutral Delay Differential Equations
Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received January 1, 2012; final manuscript received August 10, 2012; published online October 1, 2012. Assoc. Editor: Dan Negrut.
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Vyasarayani, C. P. (October 1, 2012). "Galerkin Approximations for Neutral Delay Differential Equations." ASME. J. Comput. Nonlinear Dynam. April 2013; 8(2): 021014. https://doi.org/10.1115/1.4007446
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