Application of homotopy perturbation method for solving eighth-order boundary value problems

Numerical Solution Of 12th Order Boundary Value Problems By Using Homotopy Perturbation Method

“…where (2n 1) f (x, y, y (x), , y (x)) − ′ K and y(x) are assumed real and as many as times differentiable as required for…”

“…A new perturbation method called homotopy perturbation method (HPM) was proposed by He in 1997 and systematical description in 2000 which is, in fact, a coupling of the traditional perturbation method and homotopy in topology [1][2]. This new method was further developed and improved by He and applied to nonlinear oscillators with discontinuities [3], nonlinear wave equations [4], asymptotology [5], boundary value problem [6], limit cycle and bifurcation of nonlinear problems [7] and many other subjects.…”

“…Recently various powerful mathematical methods such as variational iteration method [14][15][16][17][18][19][20][21][22][23], exp-function method [24][25], f-expansion method [24], this paper, applies the homotopy perturbation method (HPM) [1][2][3][4][5].…”

Numerical Solution of Eighth Order Boundary Value Problems by Galerkin Method with Quintic B-splines

“…al. [9] presented solution of special case of eighth order boundary value problems using variational iterational technique, Ghazala Akram and Hamood Ur Rehman [10] presented the solution of special case of eighth order boundary value problems using kernel space method there were used searching least square value method investigated for nonlinear eighth order boundary value problems, Liu and Wu [11] presented the solution of special case of eighth order boundary value problems using generalized differential quadrature rule, Koonprasert and Torvattanabum [12] presented variational iterational method for solving eighth order boundary value problems, Javidi and Golbai [13] presented HPM for solution of eighth order boundary value problems, Prorshouhi at. al.…”

Exact Solution of Klein Gordon Equation via Homotopy Perturbation Sumudu Transform Method

“…The homotopy perturbation method (HPM) introduced by He [5,6] has been widely used for solving various integral equations arising from real world modeling, for example thin film flow, heat transfer, and many others [7][8][9][10][11][12][13][14][15][16][17][18][19]. The idea behind this method is that the solution is considered as the sum of an infinite series, which converges rapidly to the exact solution.…”