Proceedings of International Conference on Applied Innovation in IT
2026/03/31, Volume 14, Issue 1, pp.221-230

Hybrid Wavelet-Adomian Decomposition Methods for Solving Nonlinear Differential Equations


Mahmood Madian Abdullah and Ekhlass Saadallah Ahmed Al-Rawi


Abstract: In this research paper, we had the study two of different types wavelets for solving some types of non-homogeneous with variable-coefficient nonlinear ordinary differential equations. Where the two wavelets were chosen from among the large number of wavelets known today in the field of function representation. The aim of studying this hybrid method, is to combine the wavelet method with the famous Adomian decomposition method, to find a more accurate and suitable approximation than using the wavelet method alone. In this research, referred to the two wavelets, after hybridizing with the Adomian decomposition method (ADM), are referred to as CAS-AM, CAS-Haar-AM. Additionally, the convergence theory of the proposed method was studied in L^2 space for CAS-Haar-AM series. The numerical results obtained when solving three examples using the proposed two-wavelet method were compared with the exact solution. Numerical stability was obtained even when the step size was large, and the results of the CAS-Haar-AM were better than using the CAS-AM. The proposed method CAS-Haar-AM is better, more accurate, and closer to the exact solution.

Keywords: CAS-Haar Wavelets, Adomian Decomposition, Ordinary Differential Equations, Operational Matrix.

DOI: Under indexing

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References:

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