**ABSTRACT**

This paper proposes a method for investigating the solvability and develop the fifth derivative block methods of step numbers for the direct solution of systems of beams equations with fully nonlinear terms differently from existing methods in literature Fifth derivative was introduced into the assumed power series basis function of the proposed. This approach produces simultaneously approximations at all the grid points for solving directly systems of beams equations. Numerical experiments such as coupled systems of beams equations, are presented to illustrate the better performance of the proposed methods than those in the recent literature. Accuracy comparison with other methods available in the recent literature are available.

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