Homotopy Perturbation Method for Solving Fourth-Order Boundary Value Problems

By Syed Tauseef Mohyud-Din, Muhammad Aslam Noor. 2007

152 citations recorded by the source corpus.

We apply the homotopy perturbation method for solving the fourth-order boundary value problems. The analytical results of the boundary value problems have been obtained in terms of convergent series with easily computable components. Several examples are given to illustrate the efficiency and implementation of the homotopy perturbation method. Comparisons are made to confirm the reliability of the method. Homotopy method can be considered an alternative method to Adomian decomposition method and its variant forms.

Subfields: Mechanics of Materials, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/c9b0e7c6c2b714cf2b6abc7c5db422f833f9b5c6

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In Mechanics of Materials

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

The exp(-Φ(ξ))-expansion method for finding travelling wave solutions of Vakhnenko-Parkes equation (2014, methodology): “, 2013a; Khan and Akbar, 2014a; Khan and Akbar, 2014b), the Homotopy perturbation method (Mohiud-Din 2007; Mohiud-Din and Noor, 2009; Mohiud-Din et al., 2010), the multiple exp-function method (Ma et al.”
Variational Iteration Method for Solving Higher-order Nonlinear Boundary Value Problems Using He's Polynomials (2008, methodology): “It is well known that series (8) is convergent for most of the cases and also the rate of convergence is dependent on L (u); see [9-15, 20, 26-31].”
VARIATION OF PARAMETERS METHOD FOR SOLVING SIXTH-ORDER BOUNDARY VALUE PROBLEMS (2009, methodology): “Noor and Mohyud-Din [4-14] used homotopy perturbation, variational iteration and variational iteration decomposition methods for solving fifth-order and other higher order boundary value problems.”
The Yang-Laplace Transform for Solving the IVPs with Local Fractional Derivative (2014, methodology): “There are analytical methods and numerical methods for solving the differential equations, such as the finite element method [6], the harmonic wavelet method [7–9], the Adomian decomposition method [10–12], the homotopy analysismethod [13, 14], the homotopy decomposition method [15, 16], the heat ba”