Hydrodynamic and hydromagnetic stability

The numerical solution of sixth-order boundary value problems by the modified decomposition method

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 examples are given to illustrate the efficiency and implementation of the homotopy perturbation method. Comparisons are made to confirm the reliability of the homotopy perturbation method. We have also considered an example where the homotopy perturbation method is not reliable.

Homotopy perturbation method for solving sixth-order boundary value problems

Linear, sixth-order boundary-value problems (special case) are solved, using polynomial splines of degree six. The spline function values at the midknots of the interpolation interval, and the corresponding values of the even-order derivatives are related through consistency relations. The algorithm developed approximates the solutions, and their higher-order derivatives, of differential equations. Two numerical illustrations are given to show the practical usefulness of the algorithm developed. It is observed that this algorithm is second-order convergent.

Spline solutions of linear sixth-order boundary-value problems

Spline solutions of linear eighth-order boundary-value problems

A family of numerical methods is developed for the solution of special nonlinear sixth-order boundary-value problems. Methods with second-, fourth-, sixth- and eighth-order convergence are contained in the family. Global extrapolation procedures on two and three grids, which increase the order of convergence, are outlined.

Numerical methods for the solution of special sixth-order boundary-value problems

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Numerical methods for the solution of special sixth-order boundary-value problems