Application of Chebyshev approximation in the process of variational iteration method for solving differential-algebraic equations

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.