Approximating system of ordinary differential-algebraic equations via derivative of Legendre polynomials operational matrices
M. Abdelhakem, Dumitru Bǎleanu, Praveen Agarwal, Hanaa Moussa
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 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.
Topics & Concepts
MathematicsLegendre polynomialsLegendre waveletAssociated Legendre polynomialsAlgebraic equationApplied mathematicsGalerkin methodLegendre functionOrdinary differential equationLegendre's equationSpectral methodMathematical analysisBasis functionAlgebraic numberJacobi polynomialsClassical orthogonal polynomialsDifferential equationOrthogonal polynomialsGegenbauer polynomialsFinite element methodNonlinear systemComputer scienceDiscrete wavelet transformThermodynamicsPhysicsQuantum mechanicsWaveletArtificial intelligenceWavelet transformFractional Differential Equations SolutionsNumerical methods for differential equationsIterative Methods for Nonlinear Equations