Direct Method to Solve Differential-Algebraic Equations by Using the Operational Matrices of Chebyshev Cardinal Functions
Abstract
A new and effective direct method to determine the numerical
solution of linear and nonlinear differential-algebraic equations
(DAEs) is proposed. The method consists of expanding the required approximate
solution as the elements of Chebyshev cardinal functions. The
operational matrices for the integration and product of the Chebyshev
cardinal functions are presented. A general procedure for forming these
matrices is given. These matrices play an important role in modelling of
problems. By using these operational matrices together, a differentialalgebraic
equation can be transformed to a system of algebraic equations.
Illustrative examples are included to demonstrate the validity and
applicability of the technique.
solution of linear and nonlinear differential-algebraic equations
(DAEs) is proposed. The method consists of expanding the required approximate
solution as the elements of Chebyshev cardinal functions. The
operational matrices for the integration and product of the Chebyshev
cardinal functions are presented. A general procedure for forming these
matrices is given. These matrices play an important role in modelling of
problems. By using these operational matrices together, a differentialalgebraic
equation can be transformed to a system of algebraic equations.
Illustrative examples are included to demonstrate the validity and
applicability of the technique.
Keywords
Linear and nonlinear differential-algebraic equations, Chebyshev cardinal function, operational matrix of integration, index reduction method
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