Document Type: Original Article


1 Department of Mathematics, Payame Noor University, tehren, iran

2 APAC Research Group, Faculty of Electrical Eng., K.N. Toosi University of Technology, Tehran, Iran

3 Department of Mathematics, Payame Noor University, Tehran, Iran

4 Department of Mechanical Engineering, University of Guilan, Rasht, Iran.



In this paper, two semi-analytical techniques are introduced to compute the solutions of differential-algebraic equations (DAEs), called the Least Squares Repetitive Homotopy Perturbation Method (LSRHPM) and the Least Squares Span Repetitive Homotopy Perturbation Method (LSSRHPM). The truncated series solution by the homotopy perturbation method only is suitable for small-time intervals. Therefore, to extend it for long time intervals, we consider the Repetitive Homotopy Perturbation Method (RHPM). To improve the accuracy of the solutions obtained by RHPM and to reduce the residual errors, least squares methods and span set are combined with RHPM. The proposed methods are applied to solve nonlinear differential-algebraic equations and optimal control problems. The results of the proposed methods are compared using some illustrative examples. The obtained results demonstrate the effectiveness and high accuracy of the new modifications. The effect of the parameters on the accuracy and performance of the methods are studied through some illustrative examples


Main Subjects