Application of He's homotopy perturbation method to linear programming problems

Closed Form Exact Solutions to the Higher Dimensional Fractional Schrodinger Equation via the Modified Simple Equation Method

“…To know the internal mechanism of complex physical phenomena exact solutions of nonlinear fractional differential equations is very much important. As a result, recently some useful methods have been established and enhanced for obtaining exact solution to the fractional evolution equations such as, the extended direct algebraic function method [3] [4], the F-expansion method [5], the Adomian decomposition method [6], the homotopy perturbation method [7] [8] [9] [10], the tanh-function method [11], the Sine-Cosine method [12], the Jacobi elliptic method [13], the finite difference method [14], the variational iteration method [15] [16], the variational method [17], the Fourier transform technique [18], the modified decomposition method [19], the Laplace transform technique [20], the operational calculus method in [21], the exp-function method [22] [23], the ( ) G G ′ -expansion method [24] [25] [26], the modified simple equation method (MSE) [27]- [34], the ( ) ( ) exp ϕ η − -expansion method [35], the sub equation method [36], the multiple exp-function method [37] [38], the simplest equation method [39], the direct algebraic function method [40] [41] [42] [43], the extended auxiliary equation method [44] etc.…”

Application of Homotopy Perturbation Method for Fuzzy Linear Systems and Comparison with Adomian’s Decomposition Method

“…This technique provides a summation of an infinite series with easily computable terms, which converges rapidly to the solution of the problem. In the literature, various authors have successfully applied this method for any kinds of different problems [37][38][39][40][41][42]. The HPM has some advantages over routine numerical methods.…”