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ERROR ANALYSIS OF VIRTUAL ELEMENT METHODS FOR THE TIME-DEPENDENT POISSON-NERNST-PLANCK EQUATIONS: 《Journal of Computational Mathematics》2025年第3期731-770,共40页Ying Yang Ya Liu Yang Liu Shi Shu; supported by the China NSF(NSFC 12161026);by the Special Fund for Scientific and Technological Bases and Talents of Guangxi(Grant No.Guike AD23026048);by the Guangxi Natural Science Foundation,China(Grant No.2020GXNSFAA159098);supported by the China NSF(NSFC 12371373);supported by the GUET Excellent Graduate Thesis Program(Grant No.2020YJSPYA02).; We discuss and analyze the virtual element method on general polygonal meshes for the time-dependent Poisson-Nernst-Planck(PNP)equations,which are a nonlinear coupled system widely used in semiconductors and ion chann...; 关键词：Virtual element method Error estimate Poisson-Nernst-Planck equations Polygonal meshes Energy projection Gummel iteration

Time-dependent Global Attractors for the Nonclassical Diffusion Equations with Fading Memory: 《Acta Mathematicae Applicatae Sinica》2025年第2期498-512,共15页Yu-ming QIN Xiao-ling CHEN; supported by the National Natural Science Foundation of China(No.12171082);the Fundamental Research Funds for the Central Universities(No.2232023G-13).; In this paper,we discuss the long-time behavior of solutions to the nonclassical diffusion equation with fading memory when the nonlinear term f satisfies critical exponential growth and the external force g(x)∈L^(2)...; 关键词：time-dependent global attractors nonclassical diffusion equation fading memory time-dependent spaces long-time behavior

TIME MULTIPOINT NONLOCAL PROBLEM FOR A STOCHASTIC SCHRÖDINGER EQUATION: 《Journal of Computational Mathematics》2025年第2期369-393,共25页Roger Pettersson Ali Sirma Tarkan Aydin; A time multipoint nonlocal problem for a Schrödinger equation driven by a cylindrical Q-Wiener process is presented.The initial value depends on a finite number of future values.Existence and uniqueness of a solution ...; 关键词：Time nonlocal problem Mild solution Cylindrical Wiener process Time discretization Abstract time-dependent stochastic Schrödinger equation Euler-Maruyama method

In an Ocean or a River:Bilinear Auto-Backlund Transformations and Similarity Reductions on an Extended Time-Dependent(3+1)-Dimensional Shallow Water Wave Equation: 《China Ocean Engineering》2025年第1期160-165,共6页GAO Xin-yi; financially supported by the Scientific Research Foundation of North China University of Technology(Grant Nos.11005136024XN147-87 and 110051360024XN151-86).; With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic...; 关键词：OCEAN RIVER extended time-dependent(3+1)-dimensional shallow water wave equation bilinear auto-Bäcklund transformation similarity reduction symbolic computation

A decoupled method for time-dependent reliability-based design optimization: 《Science China(Technological Sciences)》2025年第1期308-320,共13页Dequan ZHANG Meide YANG Xu HAN; supported by the National Science Foundation for Excellent Young Scholars(Grant No.52422507);the National Natural Science Foundation of China(Grant Nos.52305256,52275244);Postdoctoral Fellowship Program of CPSF(Grant No.GZC20230661);China Postdoctoral Science Foundation(Grant Nos.2024T170211,2023M740970)。; Time-dependent reliability-based design optimization(TRBDO)has received extensive attention because of its ability to achieve optimal solutions that help meet the requirement for whole lifecycle reliability by quantit...; 关键词：reliability-based design optimization dynamic uncertainties time-dependent reliability analysis decoupled method sequential optimization and reliability analysis

Momentum distributions of symmetric(H_(2)^(+))and asymmetric(HeH^(2+))molecular ions in a circularly polarized laser field under different ionization mechanisms: 《Chinese Physics B》2024年第12期258-263,共6页Xin-Yu Hao Shu-Juan Yan Ying Guo Jing Guo; Project supported by the Natural Science Foundation of Jilin Province(Grant No.20220101010JC);the National Natural Science Foundation of China(Grant No.12074146)。; By numerically solving the two-dimensional(2D)time-dependent Schrödinger equation(TDSE),we present photoelectron momentum distributions(PMDs)and photoelectron angular distributions(PADs)of symmetric(H_(2)^(+))and asym...; 关键词：resonance excitation time-dependent Schrödinger equation ultrafast ionization model photoelectron momentum distributions

Exact quantum dynamics for two-level systems with time-dependent driving: 《Chinese Physics B》2024年第12期79-85,共7页Zhi-Cheng He Yi-Xuan Wu Zheng-Yuan Xue; supported by the National Natural Science Foundation of China(Grant No.12275090);the Guangdong Provincial Quantum Science Strategic Initiative(Grant No.GDZX2203001);the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0302303)。; It is well known that the time-dependent Schrrödinger equation can only be solved exactly in very rare cases,even for two-level quantum systems.Thus,finding the exact quantum dynamics under a time-dependent Hamiltonia...; 关键词：quantum computation quantum control analytical solution

Advancements in Numerical Solutions:Fractal Runge-Kutta Approach to Model Time-Dependent MHD Newtonian Fluid with Rescaled Viscosity on Riga Plate: 《Computer Modeling in Engineering & Sciences》2024年第11期1213-1241,共29页Muhammad Shoaib Arif Kamaleldin Abodayeh Yasir Nawaz; support of Prince Sultan University in paying the article processing charges(APC)for this publication.; Fractal time-dependent issues in fluid dynamics provide a distinct difficulty in numerical analysis due to their complex characteristics,necessitating specialized computing techniques for precise and economical soluti...; 关键词：Fractal scheme stability convergence fractal Newtonian fluid with rescaled viscosity fluid heat generation

Painlevéintegrability,auto-Bäcklund transformations,new abundant analytic solutions including multi-soliton solutions for time-dependent extended KdV8 equation in nonlinear physics: 《Journal of Ocean Engineering and Science》2024年第5期489-507,共19页Shailendra Singh S.Saha Ray; In this paper,a new eighth-order(1+1)-dimensional time-dependent extended KdV equation has been developed.This considered equation is being found completely integrable by using the Painlevéanalysis method.Moreover,th...; 关键词：Higher-order KdV equation Painlevéanalysis Auto-Bäcklund transformation Simplified Hirota method

The Application of Thermomechanical Dynamics (TMD) to Thermoelectric Energy Generation by Employing a Low Temperature Stirling Engine: 《Journal of Applied Mathematics and Physics》2024年第9期3185-3207,共23页Hiroshi Uechi Lisa Uechi Schun T. Uechi; A thermoelectric generation Stirling engine (TEG-Stirling engine) is discussed by employing a low temperature Stirling engine and the dissipative equation of motion derived from the method of thermomechanical dynamics...; 关键词：Thermoelectric Generation Stirling Engine (TEG-Stirling Engine) Thermomechanical Dynamics (TMD) Time-Dependent Nonequilibrium Temperature Stability of Heat Engines in a Thermal State Optimal Fuel-Injection and Combustion Timings

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