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Published:
Jun 30, 2021Keywords:
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An M-stage implicit Runge-Kutta method for the numerical solution of an index-3 differential algebraic equations
Abstract
In this paper, numerical solution of Differential-Algebraic Equations with index-3 systems is considered using implicit two stage second order Runge-Kutta method. This method preserved the stability property of the numerical scheme of the differentiation-algebraic equation. The derivation of the index-3 system method using the M-stage implicit Runge-Kutta method is attempted and presented. The analysis show clearly that the spectral radius of the iteration matrix is less than one. By contraction mapping theorem, we conclude that it also converges to a solution that satisfies the Lipchitz condition. Solutions obtained and numerical error estimated, have been favorably compared with some of the existing methods and those obtained by exact solutions.
Keywords: Differential -Algebraic Equations, Index-3, M- Stage Implicit Runge-Kutta, Hessenberg form of DAEs
