Approximating system of ordinary differential-algebraic equations via derivative of Legendre polynomials operational matrices

Abstract

Legendre 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 di®erential-algebraic equations. An algorithm via those matrices has been designed. The accuracy and e±ciency of the proposed algorithm had been shown by two techniques, theoretically, via the boundedness of the approximated expansion and numerically through numerical examples.