A Dual Lagrange Multiplier Variational Iteration Method for Nonlinear Oscillators with Two-Point Boundary Conditions

This paper presents a modified variational iteration method for solving nonlinear boundary value problems arising in nonlinear oscillatory systems. By introducing dual general Lagrange multipliers, a unified correction functional is constructed for nonlinear oscillators with typical boundary constraints. The identification of the multipliers follows the standard variational theory, and rapid convergence behavior is observed in the examples. Several typical nonlinear oscillators are employed to verify the accuracy and efficiency of the method. The results show that only one iteration leads to highly accurate approximate solutions, which are in excellent agreement with the exact solutions and existing literature. The method is simple, efficient, and widely applicable, and can be further extended to solve various nonlinear problems with complex boundary constraints.