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Physics and applied mathematics form the basis for understanding natural
phenomena using differential equations depicting the flow in porous media, the motion
of viscous liquids, and the propagation of waves. These equations provide a thorough
study of physical processes, enhancing the understanding of complex applications in
engineering, technology, and medicine. This paper presents novel approximate solutions for
the Darcy-Brinkmann-Forchheimer moment equation, the Blasius equation and the FalknerSkan equation with initial / boundary conditions by using two iterative methods: the variational
iteration method and the optimal variational iteration method. The variational iteration method
is effectively developed by adding a control paramete
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