This paper introduces a novel semi-analytical technique for solving nonlinear ordinary differential equations with perturbed parameters. The proposed approach combines perturbation methods with reproducing kernel Hilbert space (RKHS) theory. The method transforms nonlinear periodic problems into systems of linear differential equations, which are then solved using RKHS techniques. We establish convergence properties and provide error estimates for the approximate solutions. Several numerical examples of Duffing oscillators demonstrate the effectiveness and accuracy of the proposed algorithm. Numerical results show that the method produces highly accurate approximate solutions, with performance comparable to established numerical techniques such as the fourth-order Runge-Kutta method.
Moradi, F. and Ranjbar, M. (2026). A Hybrid Perturbation-Reproducing Kernel Method for Numerical Solution of Duffing Oscillator. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2026.71229.3581
MLA
Moradi, F. , and Ranjbar, M. . "A Hybrid Perturbation-Reproducing Kernel Method for Numerical Solution of Duffing Oscillator", Computational Methods for Differential Equations, , , 2026, -. doi: 10.22034/cmde.2026.71229.3581
HARVARD
Moradi, F., Ranjbar, M. (2026). 'A Hybrid Perturbation-Reproducing Kernel Method for Numerical Solution of Duffing Oscillator', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2026.71229.3581
CHICAGO
F. Moradi and M. Ranjbar, "A Hybrid Perturbation-Reproducing Kernel Method for Numerical Solution of Duffing Oscillator," Computational Methods for Differential Equations, (2026): -, doi: 10.22034/cmde.2026.71229.3581
VANCOUVER
Moradi, F., Ranjbar, M. A Hybrid Perturbation-Reproducing Kernel Method for Numerical Solution of Duffing Oscillator. Computational Methods for Differential Equations, 2026; (): -. doi: 10.22034/cmde.2026.71229.3581
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