In this study, the two-point boundary value problem has been discretized using the high-order Hosoya polynomial discretization schemes to produce their corresponding Hosoya approximation equations. Next, each approximation equation can generate a system of linear equations. To get the numerical solution of the proposed problem, the direct method has been used in this study to solve the system of linear equations in various orders, namely 6, 8, 10 and 12. To validate the application of the high-order Hosoya polynomial, three examples of proposed problems have also been considered to study the accuracy of approximate solutions based on three orders of Hosoya approximation equations. Based on the results of numerical experiments, it can be pointed out that the eighth-order solution of Hosoya polynomial gives the higher accuracy as compared to sixth, tenth and twelfth order solutions. © 2022, Institute of Technology PETRONAS Sdn Bhd.