Application of He’s homotopy perturbation method for nth-order integro-differential equations

Solving <i>nth</i>-Order Integro-Differential Equations Using the Combined Laplace Transform-Adomian Decomposition Method

“…Comparing it with the HPM and VIM results given in [1,2], we notice that the result obtained by the present method is very superior (lower error combined with less number of iterations) to that obtained by HPM and VIM. From Table 2, it can be concluded that, the error decreased monotically with the increment of the integer .…”

“…Moreover, we give a comparison among the CLT-ADM, Homotopy perturbation method (HPM) [1] and the variational iteration method (VIM) [2]. The computations associated with the examples were performed using Maple 13 package.…”

“…The reader is referred to [1][2][3] for an overview of the recent work in this area. In the beginning of the 1980's, Adomian [4][5][6][7] proposed a new and fruitful method (so-called the Adomian decomposition method) for solving linear and nonlinear (algebraic, differential, partial differential, integral, etc.)…”

An analytical technique for solving general linear integral equations of the second kind and its application in analysis of flash lamp control circuit

“…The homotopy perturbation method is also very often used for seeking the solution of integral equations of different kind [25][26][27][28][29][30][31][32][33][34][35][36][37][38]. Convergence of this method in case of integral equations is considered only in few papers.…”

Numerical Solution of Linear Integro-Differential Equations

“…Therefore, many different methods are used to obtain the solution of the linear and nonlinear IDEs such as the successive approximations, Adomian decomposition, Homotopy perturbation method, Chebyshev and Taylor collocation, Haar Wavelet, Tau and Walsh series methods. [1][2][3][4][8][9][10][11][12][13][14][15][16] . In this study, by means of the homotopy analysis method (HAM), presented by Liao [5][6][7] , a general analytic approach is presented to obtain series solutions of linear IDEs:…”