Shifferaw Taye (PhD)Betely Tamiru2025-10-072025-10-072021-11https://etd.aau.edu.et/handle/123456789/7460In this paper, a state-of-the-art review is carried out on numerical methods comprising the Central Difference, Houbolt, Newmark, Wilson-𝜽, HHT-𝜶, WBZ-𝜶, Generalized-𝜶, Bathe and Piecewise Exact Methods. Three algorithms (related to Piecewise Exact Method and Power Series Method) are developed for linear and nonlinear systems. To analyze the performance of the methods, the stability and accuracy of the above-mentioned methods are studied and some solutions for illustrative examples are presented. The HHT-𝜶, WBZ-𝜶, Generalized-𝜶 and Bathe methods have controllable dissipation in higher methods. The piecewise exact method (method based on interpolation of excitation) and the proposed methods are effective in providing accurate results (compared to other methods) for the truncated modal space.en-USStructural Dynamics BETELEY TAMIRUNumerical MethodsState-of-the-ArtThesis