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In this paper, a new approach is proposed to solve nonlinear boundary value problems (BVPs). In this approach, the original nonlinear BVP transforms into a sequence of linear BVPs. Solving the proposed linear BVP sequence in a recursive manner leads to the exact solution of original problem in the form of uniformly convergent series. Hence, to obtain the exact solution, only the techniques of solving linear ordinary differential equations are employed. This confirms that the proposed method is straightforward and easy to implement. Besides, we present an efficient algorithm with low computational complexity and fast convergence rate. Through the finite iterations of the algorithm, an approximate closed-form solution is obtained for the nonlinear BVP. Finally, a numerical example is employed to demonstrate efficiency, simplicity, and high accuracy of the proposed method.