scholarly journals 4. Galerkin Approximations For The Optimal Control Of Nonlinear Delay Differential Equations

2018 ◽  
pp. 61-96
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Galerkin Approximations ◽  
Nonlinear Delay Differential Equations ◽  
Delay Differential ◽  
Nonlinear Delay

Galerkin Approximations for Higher Order Delay Differential Equations

2012 ◽  
Vol 7 (3) ◽  
Author(s):  
C. P. Vyasarayani
Keyword(s):  
Differential Equations ◽  
Lagrange Multipliers ◽  
Delay Differential Equations ◽  
Nonlinear Boundary ◽  
Boundary Constraints ◽  
Galerkin Approximations ◽  
Nonlinear Delay Differential Equations ◽  
Delay Differential ◽  
Parameter Values ◽  
Nonlinear Delay

In this work, Galerkin approximations are developed for a system of n first order nonlinear delay differential equations (DDEs) and also for an nth order nonlinear scalar DDE. The DDEs are converted into an equivalent system of partial differential equations of the same order along with the nonlinear boundary constraints. Lagrange multipliers are then introduced and explicit expressions for the Lagrange multipliers are derived to enforce the nonlinear boundary constraints. To illustrate the method, comparisons are made between the numerical solution of nonlinear DDEs and its Galerkin approximations for different parameter values.

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