Article
Engineering, Civil
Dilip Kumar Jaiswal, Naveen Kumar, Raja Ram Yadav
Summary: This study presents analytical solutions of the advection-dispersion equation (ADE) with temporal coefficients in a one-dimensional semi-infinite domain. The solutions describe the dispersion of pollutants originating from a varying or uniform pulse source, considering both groundwater flow and open medium environments. The solutions also capture the linear motion of the source and show good agreement with existing solutions. The proposed solutions, obtained through coordinate transformations and Laplace Integral Transformation Technique (LITT), offer a simplified approach for analyzing pollutant dispersion.
JOURNAL OF HYDROLOGY
(2022)
Article
Mathematics
Shalela Mohd Mahali, Amanina Setapa, Fatimah Noor Harun, Song Wang
Summary: This article compares a newly developed controlled drug release model with a time-dependent diffusion parameter to other models and validates it by fitting experimental data. The results show that the time-dependent model has the smallest fitting error and the shortest CPU time, making it the best option.
Article
Thermodynamics
Haiyan Zhang, Muhammad Nadeem, Asim Rauf, Zhao Guo Hui
Summary: This paper suggests a novel approach for solving time-fractional differential equations, which does not require any assumptions or hypotheses and is proved to be simple and effective. The proposed method demonstrates originality in directly addressing fractional partial differential equations without the need for any assumptions.
INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW
(2021)
Article
Mathematics, Applied
Xiaoxiao Geng, Hao Cheng, Wenping Fan
Summary: In this study, the analytical solution of the time-fractional telegraph equation with three kinds of nonhomogeneous boundary conditions was investigated. The authors analyzed and modified the eigenvalues and eigenfunctions derived under the Robin boundary conditions in detail, and obtained a new analytical solution. Numerical experiments confirmed the validity of the new analytical solution.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Multidisciplinary Sciences
Muhammad Naeem, Humaira Yasmin, Nehad Ali Shah, Jeevan Kafle, Kamsing Nonlaopon
Summary: In this article, an analytical solution to the time-fractional coupled Schrodinger-KdV equation is discovered using the homotopy perturbation method and the Adomian decomposition method with the Yang transformation. The solutions obtained through these techniques are numerically calculated and compared to actual solutions, demonstrating the simplicity, efficacy, and high accuracy of the methods used.
Article
Physics, Multidisciplinary
Christian Roeken, Jens Kleimann, Horst Fichtner
Summary: We present an exact and time-dependent analytical solution for the magnetic field in the inner heliosheath. The solution satisfies both the induction equation of ideal magnetohydrodynamics with infinite electric conductivity and the constraint of magnetic divergence. We assume that the magnetic field is frozen into a plasma flow similar to the interaction between the solar wind and the interstellar medium. By utilizing the ideal Ohm's law and using suitable gauge conditions, we derive a system of ordinary differential equations for the magnetic vector potential. We obtain the magnetic field by solving this system and analyzing the well-posedness of the corresponding initial-boundary value problem.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Materials Science, Multidisciplinary
Zhi-Yong Fan, Khalid K. Ali, M. Maneea, Mustafa Inc, Shao-Wen Yao
Summary: In this work, three different techniques are applied to solve the Fitzhugh-Nagumo equation, which is important for describing the propagation of electrical signals in excitable media. The methods used, including the residual power series method, homotopy perturbation method, and a modified fractional Taylor expansion, provide accurate solutions for nonlinear fractional partial differential equations. The comparison between exact and approximate solutions demonstrates the efficiency and high accuracy of these methods. Various 2D and 3D graphs are shown to support the analysis.
RESULTS IN PHYSICS
(2023)
Article
Management
Hao Zhang
Summary: This paper studies an infinite-horizon discrete-time model for dynamic learning and decision making problems. By adopting a new solution framework based on the efficient frontier of continuation-value vectors, the paper provides an analytical solution with structural properties analogous to continuous-time models and a useful tool for new discoveries in discrete-time models.
MANAGEMENT SCIENCE
(2022)
Article
Mathematics
Mu-Jung Lee, Shih-Chun Hsiao
Summary: This study investigates the impact of currents on waves and derives a third-order analytical solution for bichromatic waves on non-uniform currents. Unlike previous research, this study proposes a method that can handle multiple waves with different velocities and consider the rotational nature of the flow. The findings are important for understanding the interaction between waves and currents.
Article
Physics, Multidisciplinary
R. Schlickeiser, M. Kroeger
Summary: The study extended the analytical analysis of the SIR epidemics model to the semi-time case, which is particularly relevant for modeling later pandemic waves. It was found that the initial fraction of infected persons significantly influences the late time dependence of the epidemics, the maximum daily rate, and its peak time.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2021)
Article
Automation & Control Systems
Amir Iqbal, Sushant Veer, Yan Gu
Summary: This paper introduces a model for legged robot dynamics during locomotion on a dynamic rigid surface, along with an approximate analytical solution and a real-time walking pattern generator synthesized based on the model and solution. The model extends the classical LIP model for legged locomotion on a static surface to dynamic-surface locomotion, and stability conditions are obtained based on Floquet theory. The model is transformed into Mathieu's equation to derive an approximate analytical solution. A walking pattern generator is developed using the model and solution to efficiently plan physically feasible trajectories for quadrupedal walking. Simulations and hardware experiments confirm the accuracy and efficiency of the proposed solution, as well as the efficiency, feasibility, and robustness of the pattern generator, under various surface motions and gait parameters.
Article
Construction & Building Technology
Mingge Ye, Xiaogang Qin, Jianqiang Liu, Jianfeng Li, Pengpeng Ni, Cungang Lin
Summary: This study presents an analytical solution for calculating the responses of a pipeline affected by landslide, and evaluates the proposed approach through model testing and finite element analysis. The safety of pipelines is then assessed parametrically, and it is found that the pipe diameter and relative rigidity factor are key factors for pipeline design.
TUNNELLING AND UNDERGROUND SPACE TECHNOLOGY
(2023)
Article
Mathematics, Applied
Mamta Kapoor, Nehad Ali Shah, Wajaree Weera
Summary: The present research focuses on finding analytical solutions for time-fractional Schrodinger equations using the Shehu Transform based Adomian Decomposition Method [STADM]. Three types of time-fractional Schrodinger equations are addressed in this study. The proposed technique, which combines Shehu transform ADM and Caputo fractional derivative, allows for easy implementation and does not require discretization or numerical program development. The method is expected to be helpful in obtaining analytical solutions for complex-natured fractional PDEs and integro-differential equations, and its convergence is also mentioned.
Article
Mathematics, Applied
M. Mossa Al-Sawalha, Azzh Saad Alshehry, Kamsing Nonlaopon, Rasool Shah, Osama Y. Ababneh
Summary: In this study, the solution of the time-fractional vibration equation for large membranes is found using effective techniques like the homotopy perturbation approach and the Adomian decomposition method via the Yang transform. Numerical experiments are conducted with various initial conditions, and the findings demonstrate the competence and reliability of this analytical framework. The suggested strategies for different orders of memory-dependent derivative reduce computation size and time, and are helpful for both small and large parameters.
Article
Mathematics, Applied
Umar Farooq, Hassan Khan, Fairouz Tchier, Evren Hincal, Dumitru Baleanu, Haifa Bin Jebreen
Summary: In this note, the authors introduce an efficient computational scheme, the approximate analytical method, to solve the fractional-order Navier-Stokes model. The solutions obtained within the Liouville-Caputo operator offer a series form solution with less computational work and fast convergence rate, providing a useful approach for analyzing complex problems in related areas of science and technology.
ADVANCES IN DIFFERENCE EQUATIONS
(2021)