ADOMIAN DECOMPOSITION METHOD AND VARIATIONAL ITERATION METHOD FOR SOLVING SASA-SATSUMA EQUATION by Knier Salih, Saad Manaa

“…In this paper, two schemes are proposed to study numerical solutions of the Sasa-Satsuma nonlinear Schrödinger equation with initial conditions using the Adomian decomposition method and the variational iteration method. …”
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An Improved General Five-Component Scattering Power Decomposition Method by Yu Wang, Daqing Ge, Bin Liu, Weidong Yu, Chunle Wang

“…To address these challenges, based on the generalized five-component decomposition (G5U), we propose a hierarchical extension of the G5U method, termed ExG5U, which incorporates orientation and phase angles into the matrix rotation process. …”
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Numerical Solution of Allen – Cahn Equation by Adomian Decomposition Method by Abdulghafor Al-Rozbayani

“…The numerical results that are obtained by the Adomian decomposition method have been compared with the exact solution of  the equation shown that it is more efficient than the DuFort-Frankel method, that is illustrated through the tables and Figures.…”
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Validation of the Decomposition Method for Fast MIMO Over-the-Air Measurements by Bernhard Auinger, Thomas Zemen, Michael Gadringer, Adam Tankielun, Christoph Gagern, Wolfgang Bösch

“…To speed up the OTA test, we analyze the Decomposition Method (DM). The DM splits the throughput measurement into two parts: (1) a receiver algorithm performance tests taking the fading process into account and (2) an antenna performance test without fading process emulation. …”
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The decomposition possibility of vietnamese monazite concentrate by the pressure alkali method by Hai Son Le, Xuan Dinh Luu, Dinh Viet Nguyen, Cong Trinh Bui, Vladimir A. Karelin, Andrey A. Smorokov

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Solving Integral Equations via a hybrid method between the Modified Adomian Decomposition Method and Bee Algorithm by Noor Basam, Ahmed Entesar

“…In this paper, we used the modified Adomian decomposition(MADM) method to solve integral equations of the Volterra and Fredholm type as well, and then the Adomian method was combined with the bee algorithm(ABC) and obtained values for the parameter that improved the results obtained by solving some examples and were more accurate than the default method, These results are illustrated by calculating the maximum absolute errors (MAE) and mean squared errors (MSE). …”
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Adomian Decomposition and Variational Iteration Methods in the Context of Partial Differential Equations by Khadeejah James Audu, Lawrence Linus, Yusuph Amuda Yahaya, Sıkırulaı Akande

“…The results obtained from the numerical experiments revealed that ADM proved to be a more efficient and accurate method for solving PDEs than VIM.…”
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Economy-wide energy efficiency using a comprehensive decomposition method by D. Setyawan

“…For this goal, this research employs a multiplicative Log Mean Divisia Index II method and Spatial-Temporal Index Decomposition Analysis. …”
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A Linear Decomposition Method to Analyze and Study Pulsar Mode Changes by Longfei Hao, Zhixuan Li, Faxin Shen, Yonghua Xu, Yuxiang Huang, Kejia Lee, Qingzheng Yu, Hongguang Wang

“…In this paper, we present the linear decomposition method (LDM), which we developed to detect and analyze pulsar profile variations and mode-changing behavior. …”
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Two-dimensional contour decomposition: Decomposing mortality differences into initial difference and trend components by age and cause of death by Dmitri A. Jdanov, Domantas Jasilionis, Vladimir Shkolnikov

“…However, it does not consider the origin of this difference. Contour decomposition is the only method that does. We extend the contour decomposition method by adding one more dimension that can be used to estimate the contribution of an additional component; e.g., causes of death or educational structure. …”
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Fault Diagnosis Method of Rolling Bearing based on Fourier Decomposition Method and 1.5-dimensional Teager Energy Spectrum by Zhang Guorui, Wang Xuyuan, Guo Wenbin

“…Based on the characteristic that is the weak fault feature extraction of rolling bearing is very hard under strong background noise,a new method of rolling bearing fault diagnosis based on Fourier decomposition method（ FDM） and 1. 5- dimensional Teager energy spectrum is proposed. …”
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A Wavelet Decomposition Method for Estimating Soybean Seed Composition with Hyperspectral Data by Aviskar Giri, Vasit Sagan, Haireti Alifu, Abuduwanli Maiwulanjiang, Supria Sarkar, Bishal Roy, Felix B. Fritschi

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Flowtigs: Safety in flow decompositions for assembly graphs by Francisco Sena, Eliel Ingervo, Shahbaz Khan, Andrey Prjibelski, Sebastian Schmidt, Alexandru Tomescu

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Fault Feature Extraction Method of Gearbox based on Parameter Optimization VMD by Ding Chengjun, Fu Xiaoyang, Feng Yubo, Zhang Liang

“…The results show that this method can reduce the noise and extract the fault features of gearbox successfully，and the effect of noise reduction is better than the empirical mode decomposition method，and the extracted fault features are more obvious.…”
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Underwater acoustic signal denoising method based on DBO–VMD and singular value decomposition by A. Weiyi Chen, B. Shizhe Wang, C. Zongji Li, D. Li Dong

“…Regarding this challenge, this paper proposes a novel method called DBO–VMD–SVD. This method utilizes the Dung Beetle Optimization (DBO) algorithm to optimize Variational Mode Decomposition (VMD) and combines it with Singular Value Decomposition (SVD). …”
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Bridge Damage Identification Based on Variational Modal Decomposition and Continuous Wavelet Transform Method by Xiaobiao Jiang, Kun Ma, Jiaquan Wu, Zhengchun Li

“…The introduction of variational modal decomposition makes the extracted signal more accurate, thus enabling more accurate damage identification. …”
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Gaussian decomposition method for full waveform data of LiDAR base on neural network by Jie Liu, Xinjie Zhang, Jing Lv, Xinyu Li, Libin Du

“…Based on simulation and measured data, the decomposition success rate of this method is more than 98% with an average range accuracy of less than 1.5 cm compared to other methods. …”
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A novel LLM time series forecasting method based on integer-decimal decomposition by Lei Wang, Keyao Dong, Xiaoyong Zhao

“…Inspired by advancements in natural language processing (NLP) and computer vision (CV), large language models (LLMs) have emerged as a promising method for time series forecasting. However, fundamental differences between time series data and textual data present challenges in adapting time series for LLM-based forecasting. …”
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Two-Stage Global–Local Aerodynamic/Stealth Optimization Method Based on Space Decomposition by Wei Zhang, Lin Zhou, Bowen Shu, Xian Chen, Zhenghong Gao, Jiangtao Huang

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Research on Feature Extraction Method of Engine Misfire Fault Based on Signal Sparse Decomposition by Canyi Du, Fei Jiang, Kang Ding, Feng Li, Feifei Yu

“…Finally, a series of precise simulation signals originated from the engine dynamic finite element model, and experimental signals on the automotive engine are used to verify the proposed method’s effectiveness and antinoise performance. Additionally, comparisons with wavelet decomposition further show the proposed method to be more reliable in engine misfire diagnosis.…”
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