Homotopy Perturbation Method and Seventh-Order Boundary Value Problems

Homotopy perturbation method for solving sixth-order boundary value problems

In this paper, we apply the homotopy perturbation method for solving the sixth-order boundary value problems by reformulating them as an equivalent system of integral equations. This equivalent formulation is obtained by using a suitable transformation. The analytical results of the integral equations have been obtained in terms of convergent series with easily computable components. Several ex...

Solving the non linear system of third order boundary value problems by using He's homotopy perturbation method

Homotopy Perturbation Method with Reproducing Kernel Method for Third Order Nonlinear Boundary Value Problems

This method is based on a combination of the homotopy perturbation method (HPM) and the reproducing kernel method (RKM). The main advantages of this method is that it can overcome the restriction of the form of nonlinearity term in differential equations and improve the iterative speed of homotopy perturbation method. The solution obtained using the method takes the form of a convergent series ...

An Effective Method for Seventh-Order Boundary Value Problems

In this paper, we used the Optimal Homotopy Asymptotic Method (OHAM) to find the approximate solution of seventh order linear and nonlinear boundary value problems. The approximate solution using OHAM is compared with Variational Iteration Method (VIM) and exact solutions, an excellent agreement has been observed. The approximate solution of the equations is obtained in terms of convergent seri...

Research Article Homotopy Perturbation Method for Solving Fourth-Order Boundary Value Problems

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 ...