Solving differential-algebraic equations through variational iteration method with an auxiliary parameter

• The VIM with an auxiliary parameter is applied to differential-algebraic equations.
• Convergence of the VIM with an auxiliary parameter is studied.
• Present method provides a simple way to adjust and control the convergence region.
• Numerical results explicitly reveal the complete reliability of proposed method.
• Proposed method is particularly suitable for inverse problems.

In this study, we consider the importance of an auxiliary parameter, which is introduced into the well-known variational iteration method to obtain solutions for differential-algebraic equations. We study the convergence of the proposed method, which is called the variational iteration method with an auxiliary parameter. In addition, the proposed method is applied to two differential-algebraic equations to elucidate the solution procedure and to select the optimal auxiliary parameter. Comparisons with the results obtained by the standard variational iteration method demonstrate that the auxiliary parameter is highly effective in controlling the convergence region of the approximate solution.