  The objective of this paper is to apply the well-known exact operational
matrices (EOMs) idea for solving the Emden-Fowler equations, illustrating the
superiority of EOMs versus ordinary operational matrices (OOMs). Up to now, a
few studies have been conducted on EOMs and the differential equations solved
by them do not have high-degree nonlinearity and the reported results are not
regarded as appropriate criteria for the excellence of the new method. So, we
chose Emden-Fowler type differential equations and solved them by this method.
To confirm the accuracy of the new method and to show the preeminence of EOMs
versus OOMs, the norm1 of the residual and error function of both methods are
evaluated for multiple $m$ values, where $m$ is the degree of the Bernstein
polynomials. We reported the results in form of plots to illustrate the error
convergence of both methods to zero and also to show the primacy of the new
method versus OOMs. The obtained results have demonstrated the increased
accuracy of the new method.
