THREE-STEP SECOND DERIVATIVE HYBRID BLOCKBACKWARD DIFFERENTIATION FORMULAE FOR SOLVINGSYSTEM OF DIFFERENTIAL ALGEBRAIC EQUATIONS(DAES)

Abstract

This paper presents a new Second Derivative Hybrid Block Backward Differentiation Formulae (SDHBBDF) for solving series of engineering problems that are represented by some sets of Differential-Algebraic Equations (DAEs). The main and complimentary methods, were developed by collocation and interpolation techniques that are combined as a set of block equations. The analysis of the method showed that it is consistent, convergent, and satisfied the L-stability condition. The SDHBBDF was implemented on some physical problems of DAEs with broad intervals and the numerical results demonstrated that the method is accurate, efficient and suitable for solving DAEs. More so, the method compared favorably well with some excellent methods in the literature