This study compares the Adomian Decomposition Method (ADM) and the Variational Iteration Method (VIM) for solving nonlinear differential equations in engineering. Differential equations are essential for modeling dyna...This study compares the Adomian Decomposition Method (ADM) and the Variational Iteration Method (VIM) for solving nonlinear differential equations in engineering. Differential equations are essential for modeling dynamic systems in various disciplines, including biological processes, heat transfer, and control systems. This study addresses first, second, and third-order nonlinear differential equations using Mathematica for data generation and graphing. The ADM, developed by George Adomian, uses Adomian polynomials to handle nonlinear terms, which can be computationally intensive. In contrast, VIM, developed by He, directly iterates the correction functional, providing a more straightforward and efficient approach. This study highlights VIM’s rapid convergence and effectiveness of VIM, particularly for nonlinear problems, where it simplifies calculations and offers direct solutions without polynomial derivation. The results demonstrate VIM’s superior efficiency and rapid convergence of VIM compared with ADM. The VIM’s minimal computational requirements make it practical for real-time applications and complex system modeling. Our findings align with those of previous research, confirming VIM’s efficiency of VIM in various engineering applications. This study emphasizes the importance of selecting appropriate methods based on specific problem requirements. While ADM is valuable for certain nonlinearities, VIM’s approach is ideal for many engineering scenarios. Future research should explore broader applications and hybrid methods to enhance the solution’s accuracy and efficiency. This comprehensive comparison provides valuable guidance for selecting effective numerical methods for differential equations in engineering.展开更多
The computational techniques are a set of novel problem-solving methodologies that have attracted wider attention for their excellent performance.The handling strategies of real-world problems are artificial neural ne...The computational techniques are a set of novel problem-solving methodologies that have attracted wider attention for their excellent performance.The handling strategies of real-world problems are artificial neural networks(ANN),evolutionary computing(EC),and many more.An estimated fifty thousand to ninety thousand new leishmaniasis cases occur annually,with only 25%to 45%reported to the World Health Organization(WHO).It remains one of the top parasitic diseases with outbreak and mortality potential.In 2020,more than ninety percent of new cases reported to World Health Organization(WHO)occurred in ten countries:Brazil,China,Ethiopia,Eritrea,India,Kenya,Somalia,South Sudan,Sudan,and Yemen.The transmission of visceral leishmaniasis is studied dynamically and numerically.The study included positivity,boundedness,equilibria,reproduction number,and local stability of the model in the dynamical analysis.Some detailed methods like Runge Kutta and Euler depend on time steps and violate the physical relevance of the disease.They produce negative and unbounded results,so in disease dynamics,such developments have no biological significance;in other words,these results are meaningless.But the implicit nonstandard finite difference method does not depend on time step,positive,bounded,dynamic and consistent.All the computational techniques and their results were compared using computer simulations.展开更多
Error analysis methods in frequency domain are developed in this paper for determining the characteristic root and transfer function errors when the linear multipass algorithms are used to solve linear differential eq...Error analysis methods in frequency domain are developed in this paper for determining the characteristic root and transfer function errors when the linear multipass algorithms are used to solve linear differential equations. The relation between the local truncation error in time domain and the error in frequency domain is established, which is the basis for developing the error estimation methods. The error estimation methods for the digital simulation model constructed by using the Runge-Kutta algorithms and the linear multistep predictor-corrector algorithms are also given.展开更多
Background： Gene transcription in eukaryotie cells is collectively controlled by a large panel of ehromatin associated proteins and ChIP-seq is now widely used to locate their binding sites along the whole genome. In...Background： Gene transcription in eukaryotie cells is collectively controlled by a large panel of ehromatin associated proteins and ChIP-seq is now widely used to locate their binding sites along the whole genome. Inferring the differential binding sites of these proteins between biological conditions by comparing the corresponding ChIP-seq samples is of general interest, yet it is still a computationally challenging task. Results： Here, we briefly review the computationhl tools developed in recent years for differential binding analysis with ChIP-seq data. The methods are extensively classified by their strategy of statistical modeling and s＇cope of application. Finally, a decision tree is presented for choosing proper tools based on the specific dataset. Conclusions： Computational tools for differential binding analysis with ChIP-seq data vary significantly with respect to their applicability and performance. This review can serve as a practical guide for readers to select appropriate tools for their own datasets.展开更多
文摘This study compares the Adomian Decomposition Method (ADM) and the Variational Iteration Method (VIM) for solving nonlinear differential equations in engineering. Differential equations are essential for modeling dynamic systems in various disciplines, including biological processes, heat transfer, and control systems. This study addresses first, second, and third-order nonlinear differential equations using Mathematica for data generation and graphing. The ADM, developed by George Adomian, uses Adomian polynomials to handle nonlinear terms, which can be computationally intensive. In contrast, VIM, developed by He, directly iterates the correction functional, providing a more straightforward and efficient approach. This study highlights VIM’s rapid convergence and effectiveness of VIM, particularly for nonlinear problems, where it simplifies calculations and offers direct solutions without polynomial derivation. The results demonstrate VIM’s superior efficiency and rapid convergence of VIM compared with ADM. The VIM’s minimal computational requirements make it practical for real-time applications and complex system modeling. Our findings align with those of previous research, confirming VIM’s efficiency of VIM in various engineering applications. This study emphasizes the importance of selecting appropriate methods based on specific problem requirements. While ADM is valuable for certain nonlinearities, VIM’s approach is ideal for many engineering scenarios. Future research should explore broader applications and hybrid methods to enhance the solution’s accuracy and efficiency. This comprehensive comparison provides valuable guidance for selecting effective numerical methods for differential equations in engineering.
文摘The computational techniques are a set of novel problem-solving methodologies that have attracted wider attention for their excellent performance.The handling strategies of real-world problems are artificial neural networks(ANN),evolutionary computing(EC),and many more.An estimated fifty thousand to ninety thousand new leishmaniasis cases occur annually,with only 25%to 45%reported to the World Health Organization(WHO).It remains one of the top parasitic diseases with outbreak and mortality potential.In 2020,more than ninety percent of new cases reported to World Health Organization(WHO)occurred in ten countries:Brazil,China,Ethiopia,Eritrea,India,Kenya,Somalia,South Sudan,Sudan,and Yemen.The transmission of visceral leishmaniasis is studied dynamically and numerically.The study included positivity,boundedness,equilibria,reproduction number,and local stability of the model in the dynamical analysis.Some detailed methods like Runge Kutta and Euler depend on time steps and violate the physical relevance of the disease.They produce negative and unbounded results,so in disease dynamics,such developments have no biological significance;in other words,these results are meaningless.But the implicit nonstandard finite difference method does not depend on time step,positive,bounded,dynamic and consistent.All the computational techniques and their results were compared using computer simulations.
基金This project was supported by the National Natural Science Foundation of China (No. 19871080).
文摘Error analysis methods in frequency domain are developed in this paper for determining the characteristic root and transfer function errors when the linear multipass algorithms are used to solve linear differential equations. The relation between the local truncation error in time domain and the error in frequency domain is established, which is the basis for developing the error estimation methods. The error estimation methods for the digital simulation model constructed by using the Runge-Kutta algorithms and the linear multistep predictor-corrector algorithms are also given.
文摘Background： Gene transcription in eukaryotie cells is collectively controlled by a large panel of ehromatin associated proteins and ChIP-seq is now widely used to locate their binding sites along the whole genome. Inferring the differential binding sites of these proteins between biological conditions by comparing the corresponding ChIP-seq samples is of general interest, yet it is still a computationally challenging task. Results： Here, we briefly review the computationhl tools developed in recent years for differential binding analysis with ChIP-seq data. The methods are extensively classified by their strategy of statistical modeling and s＇cope of application. Finally, a decision tree is presented for choosing proper tools based on the specific dataset. Conclusions： Computational tools for differential binding analysis with ChIP-seq data vary significantly with respect to their applicability and performance. This review can serve as a practical guide for readers to select appropriate tools for their own datasets.
