Analyzing “Homotopy Perturbation Method for Solving Fourth-Order Boundary Value Problem”

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...

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 ...

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

Iterative method for solving a nonlinear fourth order boundary value problem

In the study of transverse vibrations of a hinged beam there arises a boundary value problem for fourth order ordinary differential equation, where a significant difficulty lies in a nonlinear term under integral sign. In recent years several authors considered finite approximation of the problem and proposed an iterative method for solving the system of nonlinear equations obtained. The essenc...

A spline method for solving fourth order singularly perturbed boundary value problem

In this paper, singularly perturbed boundary value problem of fourth order ordinary differential equation with a small positive parameter multiplying with the highest derivative of the form εu(4)(x) + p(x)u ′′ (x) + q(x)u(x) = r(x), 0 ≤ x ≤ 1, u(0) = γ0, u(1) = γ1, u ′′ (0) = η0, u ′′ (1) = η1, 0 ≤ ε ≤ 1 is considered. We have developed a numerical technique for the above problem using parametr...