Optimal variational iteration method for parametric boundary value problem

Mathematical applications in engineering have a long history. One of the most well-known analytical techniques, the optimal variational iteration method (OVIM), is utilized to construct a quick and accurate algorithm for a special fourth-order ordinary initial value problem. Many researchers have discussed the problem involving a parameter c. We solve the parametric boundary value problem that can't be addressed using conventional analytical methods for greater values of c using a new method and a convergence control parameter h. We achieve a convergent solution no matter how huge c is. For the approximation of the convergence control parameter h, two strategies have been discussed. The advantages of one technique over another have been demonstrated. Optimal variational iteration method can be seen as an effective technique to solve parametric boundary value problem.

Automated summary

The optimal variational iteration method (OVIM) is used to construct a fast and accurate algorithm for a special fourth-order ordinary initial value problem. A new method and a convergence control parameter are proposed to solve parametric boundary value problem that cannot be addressed by conventional methods. The advantages of different strategies for approximating the convergence control parameter are discussed.