Direct Method to Solve Differential-Algebraic Equations by Using the Operational Matrices of Chebyshev Cardinal Functions

A new and effective direct method to determine the numericalsolution of linear and nonlinear differential-algebraic equations(daes) is proposed. the method consists of expanding the required approximatesolution as the elements of chebyshev cardinal functions. theoperational matrices for the integration and product of the chebyshevcardinal functions are presented. a general procedure for forming thesematrices is given. these matrices play an important role in modelling ofproblems. by using these operational matrices together, a differentialalgebraicequation can be transformed to a system of algebraic equations.illustrative examples are included to demonstrate the validity andapplicability of the technique.