Approximate Solutions for Some Nonlinear Second-Order Ordinary Differential Equations Using Picard–Lindelof and Adomian Decomposition Methods
Approximate Solutions for Some Nonlinear Second-Order Ordinary Differential Equations Using Picard–Lindelof and Adomian Decomposition Methods
Anahtar Kelimeler:
Picard method; Adomian decomposition method; nonlinear differential equationsÖzet
This paper introduces a comparison between the Picard–Lindelof method (PIM) and the Adomian decomposition method (ADM) for solving second-order nonlinear differential equations. Both methods are applied to selected test problems to evaluate their accuracy and convergence rate. The Picard method is employed as an iterative scheme for successive approximations, while ADM provides a decomposition-based approach to handle nonlinearities. Numerical results indicate that both methods are effective, yet their performance varies depending on the form and complexity of the nonlinear terms. Through Examples 1–4, the paper presents a comparison between the two methods with respect to the exact solution.
