Approximate Solutions for Some Nonlinear Second-Order Ordinary Differential Equations Using Picard–Lindelof and Adomian Decomposition Methods

Wajeeda Abud Al Rashid; Mohammed Mohsen; Yahya Qaid Hasan

Approximate Solutions for Some Nonlinear Second-Order Ordinary Differential Equations Using Picard–Lindelof and Adomian Decomposition Methods

Abstract

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.

Keywords

References

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Details

Primary Language

English

Subjects

Numerical Solution of Differential and Integral Equations

Journal Section

Research Article

Authors

Wajeeda Abud Al Rashid This is me
Yemen

Mohammed Mohsen ^* This is me
Yemen

Yahya Qaid Hasan This is me
Yemen

Publication Date

June 30, 2026

Submission Date

April 22, 2026

Acceptance Date

May 20, 2026

Published in Issue

Year 2026 Volume: 3 Number: 3(1)

IZ

https://izlik.org/JA89CA63GY

Cite

RIS / Bibtex

APA

Abud Al Rashid, W., Mohsen, M., & Qaid Hasan, Y. (2026). Approximate Solutions for Some Nonlinear Second-Order Ordinary Differential Equations Using Picard–Lindelof and Adomian Decomposition Methods. Türkiye Mathematical Sciences, 3(3(1), 1-16. https://izlik.org/JA89CA63GY

AMA

1.Abud Al Rashid W, Mohsen M, Qaid Hasan Y. Approximate Solutions for Some Nonlinear Second-Order Ordinary Differential Equations Using Picard–Lindelof and Adomian Decomposition Methods. TMS. 2026;3(3(1):1-16. https://izlik.org/JA89CA63GY

Chicago

Abud Al Rashid, Wajeeda, Mohammed Mohsen, and Yahya Qaid Hasan. 2026. “Approximate Solutions for Some Nonlinear Second-Order Ordinary Differential Equations Using Picard–Lindelof and Adomian Decomposition Methods”. Türkiye Mathematical Sciences 3 (3(1): 1-16. https://izlik.org/JA89CA63GY.

EndNote

Abud Al Rashid W, Mohsen M, Qaid Hasan Y (June 1, 2026) Approximate Solutions for Some Nonlinear Second-Order Ordinary Differential Equations Using Picard–Lindelof and Adomian Decomposition Methods. Türkiye Mathematical Sciences 3 3(1) 1–16.

IEEE

[1]W. Abud Al Rashid, M. Mohsen, and Y. Qaid Hasan, “Approximate Solutions for Some Nonlinear Second-Order Ordinary Differential Equations Using Picard–Lindelof and Adomian Decomposition Methods”, TMS, vol. 3, no. 3(1), pp. 1–16, June 2026, [Online]. Available: https://izlik.org/JA89CA63GY

ISNAD

Abud Al Rashid, Wajeeda - Mohsen, Mohammed - Qaid Hasan, Yahya. “Approximate Solutions for Some Nonlinear Second-Order Ordinary Differential Equations Using Picard–Lindelof and Adomian Decomposition Methods”. Türkiye Mathematical Sciences 3/3(1) (June 1, 2026): 1-16. https://izlik.org/JA89CA63GY.

JAMA

1.Abud Al Rashid W, Mohsen M, Qaid Hasan Y. Approximate Solutions for Some Nonlinear Second-Order Ordinary Differential Equations Using Picard–Lindelof and Adomian Decomposition Methods. TMS. 2026;3:1–16.

MLA

Abud Al Rashid, Wajeeda, et al. “Approximate Solutions for Some Nonlinear Second-Order Ordinary Differential Equations Using Picard–Lindelof and Adomian Decomposition Methods”. Türkiye Mathematical Sciences, vol. 3, no. 3(1), June 2026, pp. 1-16, https://izlik.org/JA89CA63GY.

Vancouver

1.Wajeeda Abud Al Rashid, Mohammed Mohsen, Yahya Qaid Hasan. Approximate Solutions for Some Nonlinear Second-Order Ordinary Differential Equations Using Picard–Lindelof and Adomian Decomposition Methods. TMS [Internet]. 2026 Jun. 1;3(3(1):1-16. Available from: https://izlik.org/JA89CA63GY