Numerical Study for Higher Order Non-linear Boundary Value Problems Using Laplace Decomposition Method

This paper presents a numerical approach for solving higher-order nonlinear boundary value problems using the Laplace Decomposition Method (LDM). The method, constructed by combining the Laplace transform with the Adomian decomposition technique, allows the governing equations to be handled without linearization or the introduction of small parameters. To demonstrate the applicability of the approach, we consider nonlinear boundary value problems of twelfth, thirteenth, and fourteenth orders. For each problem, approximate series solutions are obtained and compared with known exact solutions and results available in the literature. The numerical results show that the proposed method yields accurate approximations with rapid convergence across the computational domain. All computations are carried out using Maple 2022, confirming that the method is both reliable and computationally efficient for higher-order nonlinear boundary value problems.