A Double Decomposition Method for Solving Systems of Two-Point Boundary-Value Problems

The current manuscript introduces an efficient modification scheme, based on the Adomian decomposition method, for the numerical solution of systems of two-point boundary-value problems. Indeed, this introduced method is characterized by high computational flexibility in accurately solving both the systems of linear and nonlinear differential equations with two-point boundary conditions. Moreover, to assess the robustness of these schemes, several test numerical examples, including a well-known model in fluid dynamics, have been sought and treated. Comparatively, the results from the proposed method have been compared with those of the available exact solutions and those of deployed existing numerical methods in the literature. Lastly, in the presence of the methods used for comparison, the assessment of this method turned out to be positive, with rapid convergence and high precision speedily attained.