Abstract
In this paper, we use Chebyshev approximations in the process of He’s variational iteration method for finding the solution of differential-algebraic equations. This allows us to make integration at each of the iterations possible and at the same time, obtain a good accuracy in a reasonable number of iterations. Numerical results show that using Chebyshev approximation is much more efficient than using Taylor approximation which is more popular. First, an index reduction technique is implemented for semi-explicit differentialalgebraic equations, then the obtained problem is solved by He’s variational iteration method. The scheme is tested for some high index differential-algebraic equations and the results demonstrate reliability and efficiency of the proposed method.
Highlights
Many physical problems are governed by a system of differential-algebraic equations (DAEs), and finding the solution of these equations has been the subject of many investigations in recent years
In [15] the variational iteration method (VIM) has been implemented for finding the solution of differentialalgebraic equations
The results are compared with the VIM using Taylor series
Summary
Many physical problems are governed by a system of differential-algebraic equations (DAEs), and finding the solution of these equations has been the subject of many investigations in recent years. The method introduces a reliable and efficient process for a wide variety of scientific and engineering applications. It is well known that the eigenfunctions of certain singular Sturm-Liouville problems allow the approximation of functions C [a, b] where truncation error approaches zero faster than any negative power of the number of basic functions used in the approximation, as that number (order of truncation ) tends to infinity [16]. This phenomenon is usually referred to as '' spectral accuracy ''. Tk k 0 which are eigenfunctions of singular Sturm-Liouville problem:
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