<p>This study presents a numerical approach for solving systems of second-order differential equations (DEs) and integro-differential equations (IDEs) using a collocation method based on Haar functions. The method approximates second-order derivatives using Haar functions, and determines first-order derivatives and the unknown function by integration and application of initial conditions. The collocation points convert the system into algebraic equations, which are solved using Gauss elimination to obtain the Haar coefficients. The solution is then derived using these coefficients. The method’s effectiveness is demonstrated through various test problems, with results showing high accuracy and minimal error. A comparison of exact and approximate solutions confirms the accuracy of the proposed method, making it a reliable tool for solving such systems.</p>