Abdelhakem, M.Baleanu, D.Agarwal, P.Moussa, Hanaa2024-02-012025-09-182024-02-012025-09-182023Abdelhakem M.;...et.al. (2023). "Approximating system of ordinary differential-algebraic equations via derivative of Legendre polynomials operational matrices", International Journal of Modern Physics C, Vol.34, No.3.0129-18311793-6586https://doi.org/10.1142/S0129183123500365https://hdl.handle.net/20.500.12416/14478Agarwal, Praveen/0000-0001-7556-8942; Abdelhakem, Mohamed/0000-0001-7085-1685; Moussa, Hanaa/0000-0001-9181-0284Legendre polynomials' first derivatives have been used as the basis function via the pseudo-Galerkin spectral method. Operational matrices for derivatives have been used and extended to deal with the system of ordinary differential-algebraic equations. An algorithm via those matrices has been designed. The accuracy and efficiency of the proposed algorithm had been shown by two techniques, theoretically, via the boundedness of the approximated expansion and numerically through numerical examples.eninfo:eu-repo/semantics/closedAccessSpectral ApproximationPseudo-Galerkin Spectral MethodOperational MatricesFirst Derivatives Legendre PolynomialsOrdinary Differential-Algebraic EquationsGlobal Error AnalysisArticle10.1142/S01291831235003652-s2.0-85139788657