<p>This article presents a computational method to solve the Singular Perturbed second-order boundary value problem that occurs in chemical flow reactor theory. The proposed method does not require the matrix inversion for the numerical convergence of the boundary value problem. The numerical solution of the proposed method in this article reflects the asymptotic behavior of the solution of the given boundary value problem. It is an optimal computational method. The computational rate of the order of convergence of the method is given. The computational error at the right end boundary is also given in this article. This method works well for small values of the singular perturbation parameter and even for large step sizes. The numerical and graphical results show the performance of the method.</p>