An Optimal Choice of Initial Solutions in the Homotopy Perturbation Method

Implementation of the Homotopy Perturbation Sumudu Transform Method for Solving Klein-Gordon Equation

“…There are several analytical have been presented in the literature to solve fractional partial differential equations (FPDEs), such as the Fourier transform method [1], the fractional Greens function method [2], the Mellin transform method and the Laplace transform method [3] [4], the Sumudu transform method [5]. Recently, several numerical methods have been introduced for this purpose, such as: the homotopy perturbation method (HPM) has first proposed by He [6]- [8], the Modified homotopy perturbation method (MHPM) [9], the differential transform method (DTM) [10], the variational iteration method (VIM) [11] [12], the homotopy analysis method (HAM) [13] [14], the Sumudu decomposition method [15], the Adomian decomposition method [16] [17].…”

RETRACTED：Implementation of the Homotopy Perturbation Sumudu Transform Method for Solving Klein-Gordon Equation

“…Some of these analytical methods are the Fourier transform method [1], the fractional Green function method [2], the popular Laplace transform method [3] [4], the Sumudu transform method [5], the iteration method [4], the Mellin transform method and the method of orthogonal polynomials [3]. Some numerical methods are also popular, such as the homotopy perturbation method (HPM) [6]- [8], the modified homotopy perturbation method (MHPM) [9], the differential transform method (DTM) [10], the variational iteration method (VIM) [11] [12], the homotopy analysis method (HAM) [13] [14], the Sumudu decomposition method [15] and the Adomian decomposition method [16] [17].…”

Homotopy Perturbation Transform Method for Solving Korteweg-DeVries (KDV) Equation

“…In 1992. He [5][6][7][8][9][10][11][12][13][14][15][16][17][18] developed the homotopy perturbation method (HPM) by merging the standard homotopy and perturbation for solving various physical problems. The authors have applied this method successfully to problems arising in mathematics engineering.…”