Homotopy perturbation method in quantum mechanical problems

New Exact Solutions of the Conformable Space-Time Sharma–Tasso–Olver Equation Using Two Reliable Methods

“…Step 2: The value of the positive integer N in solution (6) can be computed by balancing the highest-order derivative term with the nonlinear terms of the highest order occurring in Equation (5). The degree formulas of some terms are given as…”

“…Several powerful methods based on using symbolic software packages such as Mathematica or Maple 17 have been proposed and developed to analytically solve NPDEs. Some examples of approaches for obtaining approximate solutions in an analytical form to NPDEs are the Adomian decomposition method (ADM) [1,2], the variational iteration method (VIM) [3,4], the differential transform method (DTM) [5], and the homotopy perturbation method (HPM) [6,7]. Some algorithms for obtaining explicit exact solutions of NPDEs are, for instance, the ( G G )-expansion method [8,9], the ( G G , 1 G )-expansion method [10], the fractional Riccati expansion method [11,12], the improved extended tanh-coth method [13], the Kudryashov method [14,15], and the sub-equation method [16,17].…”

Study of strongly nonlinear oscillators using the Aboodh transform and the homotopy perturbation method

“…According to the homotopy perturbation method [21,17,26], we may expand x(t) in power of an embedded parameter p (0 ≤ p ≤ 1) as, x(t) = ∞ n=0 p n x n (t) and nonlinear term N x(t) = ∞ n=0 p n H n (x), where He's polynomial H n (x) can be written as,…”

Exact Traveling Wave Solutions of Certain Nonlinear Partial Differential Equations Using the G′/G2Sirisubtawee1, Koonprasert2 2018Advances in Mathematical Physics440190View full textAdd to dashboardCite

“…The methods for obtaining exact explicit solutions of NPDEs are, for example, the ( / )-expansion method [6][7][8], the ( / , 1/ )-expansion method [9][10][11], the novel ( / )-expansion method [12], the tanh-function method [13], the exp-function method [14,15], the F-expansion method [16], Hirota's direct method [17,18], Kudryashov method [19,20], and the extended auxiliary equation method [21]. Examples of the methods for obtaining analytical approximate solutions to NPDEs are the variational iteration method [22,23] (VIM), the Adomian decomposition method [24,25] (ADM), the homotopy perturbation method [26,27] (HPM), and the reduced differential transform method [28]. In addition, the examples of useful methods for solving NPDEs numerically are the generalized finite difference method [29], the finite volume method [30], the finite element method [31], the spectral collocation method [32], and the Galerkin finite element method [33].…”