As a numerical method to solve nonlinear two-point boundary value problems, the shooting method is well-known. Recently, an efficient shooting algorithm has been proposed which retains local quadratic convergence in the presence of the discretization error of numerical integration. In this paper, it is shown that by combining the shooting algorithm with Richardson extrapolation, accurate numerical solutions can be obtained with relatively few computations. Numerical examples are given to confirm the effectiveness of the proposed approach.

ordinary differential equation, nonlinear two-point boundary value problem, shooting method, Richardson extrapolation, Newton’s method.