<p>This paper presents a robust modified Adomian decomposition method (MADM) for solving linear and nonlinear higher-order boundary value problems (BVPs), ranging from third-order to <i>n</i>-th order, with two-point or multi-point boundary conditions. The proposed method streamlines the solution process by eliminating the computational complexities inherent in traditional numerical approaches. A rigorous theoretical analysis is conducted to establish the uniform convergence and Lyapunov stability of the proposed scheme. The efficacy of the method is further validated through a series of numerical examples, encompassing diverse cases such as high-order nonlinear BVPs under various boundary conditions. The results demonstrate that the proposed methodology is highly accurate, computationally efficient, and exhibits rapid convergence; this establishes it as a superior alternative to more resource-intensive numerical methods.</p>