Application of the Exact Operational Matrices For Solving the Emden-Fowler Equations, Arising in ‎Astrophysics‎

The objective of this paper is applying the well-known exactoperational matrices (eoms) idea for solving the emden-fowlerequations, illustrating the superiority of eoms over ordinaryoperational matrices (ooms). up to now, a few studies have beenconducted on eoms ; but the solved differential equations did nothave high-degree nonlinearity and the reported results could notstrongly show the excellence of this new method. so, we choseemden-fowler type differential equations and solved them utilizingthis method. to confirm the accuracy of the new method and to showthe preeminence of eoms over ooms, the norm 1 of the residual anderror function for both methods are evaluated for multiple $m$values, where $m$ is the degree of the bernstein polynomials. wereport the results by some plots to illustrate the errorconvergence of both methods to zero and also to show the primacyof the new method versus ooms. the obtained results demonstratethe increased accuracy of the new ‎method.‎