Application of He’s variational iteration method for solution of differential-algebraic equations

Application of Chebyshev Approximation in the Process of Variational Iteration Method for Solving Differentialalgebraic Equations

“…So after 16 iterations, (15) and (16) Chebyshev series with the same number of terms. Using (15) and (16), after 16 iterations, we obtain …”

“…The VIM was successfully applied to autonomous ordinary and partial differential equations [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Recently in [15] the VIM has been implemented for finding the solution of differentialalgebraic equations. To avoid tedious integration, in the latter paper the Taylor approximation is used.…”

An efficient scheme for solving a system of time- fractional order differential-algebraic equations by using fractional Laplace iteration method

“…In recent years, many researchers have focused on the numerical solution of fractional differential -algebraic equations. Some numerical methods have been developed, such as implicit RungeKutta method [5], Padé approximation method [6][7][8][9], homotopy perturbation method [10][11][12][13][14], Adomian decomposition method [15][16][17][18][19], homotopy analysis method [20][21], variation iteration method [22][23][24], homotopy analysis transform method [25]. In 2013, Habibolla et al [26] presented an alternative approach based on Laplace iterative method (LIM) for finding series solutions to linear and nonlinear systems of PDEs.…”

Analytical Approach of Differential-Algebraic Equations of Fractional Order Via Homotopy Perturbation Method

“…In recent years, much research has been focused on the numerical solution of systems of differentialalgebraic equations. Some numerical methods have been developed, such as implicit Runge-Kutta method [1], Padé approximation method [2,4,5,16], homotopy perturbation method [14], Adomain decomposition method [8,9] and variation iteration method [15]. Consider the following system of differential-algebraic equations of fractional order [18] In this paper, the homotopy perturbation method (HPM) is used to give a semi-analytical solution of the problem (1.1).…”