Abstract
This research investigates differential-algebraic equations with higher index (index four). Specifically, a functional analytic approach is proposed to find the solution of (index four) Hessenberg differential-algebraic equations (DAEs). The approximate solution of the proposed functional approach for a suitable separable Hilbert space is obtained with the help of the direct optimisation technique and Ritz basis functions method. Illustrations have been ranked from an 8 × 8 test system of index-four Hessenberg linear DAEs to a 4 × 4 DAE of rotating masses as well as an 8 × 8 differential-algebraic generator model, where it reformulated index-four linear Hessenberg DAEs. Their approximate solutions were obtained using the present approach with comparisons. The numerical results demonstrate the simplicity of the proposed approach and express suitable accuracy and efficiency.
Highlights
Many life applications can be modelled as differential-algebraic systems, including optimal control problems, constrained robotic systems, and constrained electrical networks [1,2,3]
To determine an equivalent ordinary differential equation, the minimum number of times that the algebraic constraint of differential-algebraic equations (DAEs) must be differentiated to time is represented with the frequently used differentiation index [5]. e higher index DAEs present a greater challenge in being solved than those in the lower index system because it makes applications more cumbersome [6]
To solve higher index Hessenberg linear DAE systems, this article develops an analytical approximation method to be efficiently and implemented. It is based on the functional analytical theory, which will help to determine a functional with critical points that serve as solutions for the fourth index Hessenberg DAEs and vice versa
Summary
Many life applications can be modelled as differential-algebraic systems, including optimal control problems, constrained robotic systems, and constrained electrical networks [1,2,3]. E higher index DAEs present a greater challenge in being solved than those in the lower index system because it makes applications more cumbersome [6]. To solve higher index (index four) Hessenberg linear DAE systems, this article develops an analytical approximation method to be efficiently and implemented. It is based on the functional analytical theory, which will help to determine a functional with critical points that serve as solutions for the fourth index Hessenberg DAEs and vice versa. To determine the solution of the variational formulation for unknown parameters, the method uses a direct method of calculus of variation. Solving the linear algebraic system obtains the unknown parameters
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