Uniqueness and error estimates for solutions to higher-order boundary value problems

Little work has been done for the error estimates of the homotopy analysis method. For general 2nth-order linear and nonlinear differential equations with Lidstone boundary conditions, we obtain sharp upper bounds for the absolute error of the approximations given by the homotopy analysis method. To achieve this goal, the existence and uniqueness of solutions to these differential equations are considered. Numerical results confirm the theoretical predictions.