Optimal variational iteration method for parametric boundary value problem

Abstract

<abstract> <p>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 <italic>c</italic>. We solve the parametric boundary value problem that can't be addressed using conventional analytical methods for greater values of <italic>c</italic> using a new method and a convergence control parameter <italic>h</italic>. We achieve a convergent solution no matter how huge <italic>c</italic> is. For the approximation of the convergence control parameter <italic>h</italic>, 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.</p> </abstract>