Advanced Mathematical Models & Applications

This paper focuses on the numerical solution of linear second-order differential equation boundary value problems using the Piecewise Constant Argument Method (PCAM). Initially, we formulate an initial value problem with piecewise constant arguments corresponding to the original differential equation, which guarantees a unique solution. Then, the shooting method is employed to transform the boundary value problem into initial value problems, allowing computation of approximate solutions. To validate the effectiveness and precision of the proposed approach, several differential equations derived from different physical models with specified boundary conditions are solved. Finally, the results are compared with recent numerical approximations, demonstrating that the proposed method is both accurate and computationally efficient.