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Prediction of ILI following the COVID-19 pandemic in China by using a partial differential equation
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作者 Xu Zhang Yu-Rong Song Ru-Qi Li 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第11期118-128,共11页
The COVID-19 outbreak has significantly disrupted the lives of individuals worldwide.Following the lifting of COVID-19 interventions,there is a heightened risk of future outbreaks from other circulating respiratory in... The COVID-19 outbreak has significantly disrupted the lives of individuals worldwide.Following the lifting of COVID-19 interventions,there is a heightened risk of future outbreaks from other circulating respiratory infections,such as influenza-like illness(ILI).Accurate prediction models for ILI cases are crucial in enabling governments to implement necessary measures and persuade individuals to adopt personal precautions against the disease.This paper aims to provide a forecasting model for ILI cases with actual cases.We propose a specific model utilizing the partial differential equation(PDE)that will be developed and validated using real-world data obtained from the Chinese National Influenza Center.Our model combines the effects of transboundary spread among regions in China mainland and human activities’impact on ILI transmission dynamics.The simulated results demonstrate that our model achieves excellent predictive performance.Additionally,relevant factors influencing the dissemination are further examined in our analysis.Furthermore,we investigate the effectiveness of travel restrictions on ILI cases.Results can be used to utilize to mitigate the spread of disease. 展开更多
关键词 partial differential equations INFLUENZA SIS model PREDICTION
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THE EXACT MEROMORPHIC SOLUTIONS OF SOME NONLINEAR DIFFERENTIAL EQUATIONS
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作者 刘慧芳 毛志强 《Acta Mathematica Scientia》 SCIE CSCD 2024年第1期103-114,共12页
We find the exact forms of meromorphic solutions of the nonlinear differential equations■,n≥3,k≥1,where q,Q are nonzero polynomials,Q■Const.,and p_(1),p_(2),α_(1),α_(2)are nonzero constants withα_(1)≠α_(2).Co... We find the exact forms of meromorphic solutions of the nonlinear differential equations■,n≥3,k≥1,where q,Q are nonzero polynomials,Q■Const.,and p_(1),p_(2),α_(1),α_(2)are nonzero constants withα_(1)≠α_(2).Compared with previous results on the equation p(z)f^(3)+q(z)f"=-sinα(z)with polynomial coefficients,our results show that the coefficient of the term f^((k))perturbed by multiplying an exponential function will affect the structure of its solutions. 展开更多
关键词 Nevanlinna theory nonlinear differential equations meromorphic functions entire functions
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Results Involving Partial Differential Equations and Their Solution by Certain Integral Transform
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作者 Rania Saadah Mohammed Amleh +2 位作者 Ahmad Qazza Shrideh Al-Omari Ahmet Ocak Akdemir 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第2期1593-1616,共24页
In this study,we aimto investigate certain triple integral transformand its application to a class of partial differentialequations.We discuss various properties of the new transformincluding inversion, linearity, exi... In this study,we aimto investigate certain triple integral transformand its application to a class of partial differentialequations.We discuss various properties of the new transformincluding inversion, linearity, existence, scaling andshifting, etc. Then,we derive several results enfolding partial derivatives and establish amulti-convolution theorem.Further, we apply the aforementioned transform to some classical functions and many types of partial differentialequations involving heat equations,wave equations, Laplace equations, and Poisson equations aswell.Moreover,wedraw some figures to illustrate 3-D contour plots for exact solutions of some selected examples involving differentvalues in their variables. 展开更多
关键词 ARA transform double ARA transform triple ARA transform partial differential equations integral transform
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Meta-Auto-Decoder:a Meta-Learning-Based Reduced Order Model for Solving Parametric Partial Differential Equations
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作者 Zhanhong Ye Xiang Huang +1 位作者 Hongsheng Liu Bin Dong 《Communications on Applied Mathematics and Computation》 EI 2024年第2期1096-1130,共35页
Many important problems in science and engineering require solving the so-called parametric partial differential equations(PDEs),i.e.,PDEs with different physical parameters,boundary conditions,shapes of computational... Many important problems in science and engineering require solving the so-called parametric partial differential equations(PDEs),i.e.,PDEs with different physical parameters,boundary conditions,shapes of computational domains,etc.Typical reduced order modeling techniques accelerate the solution of the parametric PDEs by projecting them onto a linear trial manifold constructed in the ofline stage.These methods often need a predefined mesh as well as a series of precomputed solution snapshots,and may struggle to balance between the efficiency and accuracy due to the limitation of the linear ansatz.Utilizing the nonlinear representation of neural networks(NNs),we propose the Meta-Auto-Decoder(MAD)to construct a nonlinear trial manifold,whose best possible performance is measured theoretically by the decoder width.Based on the meta-learning concept,the trial manifold can be learned in a mesh-free and unsupervised way during the pre-training stage.Fast adaptation to new(possibly heterogeneous)PDE parameters is enabled by searching on this trial manifold,and optionally fine-tuning the trial manifold at the same time.Extensive numerical experiments show that the MAD method exhibits a faster convergence speed without losing the accuracy than other deep learning-based methods. 展开更多
关键词 Parametric partial differential equations(PDEs) META-LEARNING Reduced order modeling Neural networks(NNs) Auto-decoder
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Pseudo S-Asymptotically(ω,c)-Periodic Solutions to Fractional Differential Equations of Sobolev Type
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作者 MAO Hang-ning CHANG Yong-kui 《Chinese Quarterly Journal of Mathematics》 2024年第3期295-306,共12页
In this paper,we firstly recall some basic results on pseudo S-asymptotically(ω,c)-periodic functions and Sobolev type fractional differential equation.We secondly investigate some existence of pseudo S-asymptotical... In this paper,we firstly recall some basic results on pseudo S-asymptotically(ω,c)-periodic functions and Sobolev type fractional differential equation.We secondly investigate some existence of pseudo S-asymptotically(ω,c)-periodic solutions for a semilinear fractional differential equations of Sobolev type.We finally present a simple example. 展开更多
关键词 Pseudo S-asymptotically(ω c)-periodic functions Evolution equations Sobolev type Fractional differential equations Existence and uniqueness
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Machine learning of partial differential equations from noise data
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作者 Wenbo Cao Weiwei Zhang 《Theoretical & Applied Mechanics Letters》 CAS CSCD 2023年第6期441-446,共6页
Machine learning of partial differential equations(PDEs)from data is a potential breakthrough for addressing the lack of physical equations in complex dynamic systems.Recently,sparse regression has emerged as an attra... Machine learning of partial differential equations(PDEs)from data is a potential breakthrough for addressing the lack of physical equations in complex dynamic systems.Recently,sparse regression has emerged as an attractive approach.However,noise presents the biggest challenge in sparse regression for identifying equations,as it relies on local derivative evaluations of noisy data.This study proposes a simple and general approach that significantly improves noise robustness by projecting the evaluated time derivative and partial differential term into a subspace with less noise.This method enables accurate reconstruction of PDEs involving high-order derivatives,even from data with considerable noise.Additionally,we discuss and compare the effects of the proposed method based on Fourier subspace and POD(proper orthogonal decomposition)subspace.Generally,the latter yields better results since it preserves the maximum amount of information. 展开更多
关键词 partial differential equation Machine learning Sparse regression Noise data
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The Fractional Investigation of Some Nonlinear Partial Differential Equations by Using an Efficient Procedure
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作者 Fairouz Tchier Hassan Khan +2 位作者 Shahbaz Khan Poom Kumam Ioannis Dassios 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第6期2137-2153,共17页
The nonlinearity inmany problems occurs because of the complexity of the given physical phenomena.The present paper investigates the non-linear fractional partial differential equations’solutions using the Caputo ope... The nonlinearity inmany problems occurs because of the complexity of the given physical phenomena.The present paper investigates the non-linear fractional partial differential equations’solutions using the Caputo operator with Laplace residual power seriesmethod.It is found that the present technique has a direct and simple implementation to solve the targeted problems.The comparison of the obtained solutions has been done with actual solutions to the problems.The fractional-order solutions are presented and considered to be the focal point of this research article.The results of the proposed technique are highly accurate and provide useful information about the actual dynamics of each problem.Because of the simple implementation,the present technique can be extended to solve other important fractional order problems. 展开更多
关键词 Fractional calculus laplace transform laplace residual power series method fractional partial differential equation power series fractional power series
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Oscillation for Solutions of Systems of High Order Partial Differential Equations of Neutral Type 被引量:8
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作者 LIN Wen-xian(Department of Mathematics, Hanshan Teacher’s College, Chaozhou 521041, China) 《Chinese Quarterly Journal of Mathematics》 CSCD 2003年第2期168-174,共7页
In this paper, sane sufficient conditions are obtained for the oscillation for solutions of systems of high order partial differential equations of neutral type.
关键词 neutral type system of partial differential equations OSCILLATION
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Finite-time consensus of multi-agent systems driven by hyperbolic partial differential equations via boundary control 被引量:2
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作者 Xuhui WANG Nanjing HUANG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2021年第12期1799-1816,共18页
The leaderless and leader-following finite-time consensus problems for multiagent systems(MASs)described by first-order linear hyperbolic partial differential equations(PDEs)are studied.The Lyapunov theorem and the un... The leaderless and leader-following finite-time consensus problems for multiagent systems(MASs)described by first-order linear hyperbolic partial differential equations(PDEs)are studied.The Lyapunov theorem and the unique solvability result for the first-order linear hyperbolic PDE are used to obtain some sufficient conditions for ensuring the finite-time consensus of the leaderless and leader-following MASs driven by first-order linear hyperbolic PDEs.Finally,two numerical examples are provided to verify the effectiveness of the proposed methods. 展开更多
关键词 finite-time consensus hyperbolic partial differential equation(PDE) leaderless multi-agent system(MAS) leader-following MAS boundary control
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Data-driven and physical-based identification of partial differential equations for multivariable system 被引量:1
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作者 Wenbo Cao Weiwei Zhang 《Theoretical & Applied Mechanics Letters》 CSCD 2022年第2期127-131,共5页
Data-driven partial differential equation identification is a potential breakthrough to solve the lack of physical equations in complex dynamic systems.However,existing equation identification methods still cannot eff... Data-driven partial differential equation identification is a potential breakthrough to solve the lack of physical equations in complex dynamic systems.However,existing equation identification methods still cannot effectively identify equations from multivariable complex systems.In this work,we combine physical constraints such as dimension and direction of equation with data-driven method,and successfully identify the Navier-Stocks equations from the flow field data of Karman vortex street.This method provides an effective approach to identify partial differential equations of multivariable complex systems. 展开更多
关键词 partial differential equation identification DATA-DRIVEN Multivariable system Dimensional analysis
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A SOLVING METHOD FOR A SYSTEM OF PARTIAL DIFFERENTIAL EQUATIONS WITH AN APPLICATION TO THE BENDING PROBLEM OF A THICK PLATE
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作者 尹益辉 陈刚 陈裕泽 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1999年第11期1259-1265,共7页
A theorem of solving a system of linear non-homogeneous differential equations through integrating and adding its basic solutions is put forward and proved, the mathematical role and physical nature of the theorem is ... A theorem of solving a system of linear non-homogeneous differential equations through integrating and adding its basic solutions is put forward and proved, the mathematical role and physical nature of the theorem is interpreted briefly. As an example, the theorem is applied to solve the problem of thermo-force bending of a thick plate. 展开更多
关键词 partial differential equations integrating method thick plate thermo-force bending
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FORCED OSCILLATIONS OF BOUNDARY VALUE PROBLEMS OF HIGHER ORDER FUNCTIONAL PARTIAL DIFFERENTIAL EQUATIONS
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作者 靳明忠 董莹 李崇孝 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1996年第9期889-900,共12页
In this paper we study the forced oscillations of boundary value problems of a class of higher order functional partial differential equations.The principal tool is an everaging techniqe which enables one to establish... In this paper we study the forced oscillations of boundary value problems of a class of higher order functional partial differential equations.The principal tool is an everaging techniqe which enables one to establish oscillation in terms of related functional differential inequallities. 展开更多
关键词 higher order functional partial differential equation boundary value problems forced oscillation
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A SYMBOLIC COMPUTATION METHOD TO DECIDE THE COMPLETENESS OF THE SOLUTIONS TO THE SYSTEM OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS
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作者 张鸿庆 谢福鼎 陆斌 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第10期1134-1139,共6页
A symbolic computation method to decide whether the solutions to the system Of linear partial differential equation is complete via using differential algebra and characteristic set is presented. This is a mechanizati... A symbolic computation method to decide whether the solutions to the system Of linear partial differential equation is complete via using differential algebra and characteristic set is presented. This is a mechanization method, and it can be carried out on the computer in the Maple environment. 展开更多
关键词 differential algebra system of partial differential equation symbolic computation characteristic set
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SINGULARLY PERTURBED METHODS IN THE THEORY OF OPTIMAL CONTROL OF SYSTEMS GOVERNED BY PARTIAL DIFFERENTIAL EQUATIONS
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作者 田根宝 林宗池 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1994年第8期713-719,共7页
In this paper, the various problems associaled with the optimal control of systemsgoverned by partial differential equations are introduced by using singularly perturbedmethods for analysis based on stale equations,... In this paper, the various problems associaled with the optimal control of systemsgoverned by partial differential equations are introduced by using singularly perturbedmethods for analysis based on stale equations, or the cost funtction and also stateequations defined in perturbed domains. 展开更多
关键词 optimal control perturbation techniques partial differential equations
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Remarks on Oscillation for Systems of High Order Partial Differential Equations of Neutral Type
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作者 LIN Wen-xian 《Chinese Quarterly Journal of Mathematics》 CSCD 2009年第4期537-542,共6页
In this paper, some sufficient conditions are obtained for the oscillation for solutions of systems of high order partial differential equations of neutral type.
关键词 neutral type system of partial differential equations OSCILLATION
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Numerical Solution of Nonlinear System of Partial Differential Equations by the Laplace Decomposition Method and the Pade Approximation
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作者 Magdy Ahmed Mohamed Mohamed Shibl Torky 《American Journal of Computational Mathematics》 2013年第3期175-184,共10页
In this paper, Laplace decomposition method (LDM) and Pade approximant are employed to find approximate solutions for the Whitham-Broer-Kaup shallow water model, the coupled nonlinear reaction diffusion equations and ... In this paper, Laplace decomposition method (LDM) and Pade approximant are employed to find approximate solutions for the Whitham-Broer-Kaup shallow water model, the coupled nonlinear reaction diffusion equations and the system of Hirota-Satsuma coupled KdV. In addition, the results obtained from Laplace decomposition method (LDM) and Pade approximant are compared with corresponding exact analytical solutions. 展开更多
关键词 NONLINEAR system of partial differential equationS The LAPLACE Decomposition Method The Pade Approximation The COUPLED system of the Approximate equationS for Long WATER Waves The Whitham Broer Kaup Shallow WATER Model The system of Hirota-Satsuma COUPLED KdV
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Existence of Periodic Solutions for Generalized Liénard-Typed Functional Differential Equations
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作者 贺小明 葛渭高 单文锐 《Journal of Beijing Institute of Technology》 EI CAS 2002年第3期325-328,共4页
The existence of periodic solutions for a kind of generalized Liénard typed functional differential equation is studied. By means of the continuation theorem of coincidence degree theory, existence criteria are ... The existence of periodic solutions for a kind of generalized Liénard typed functional differential equation is studied. By means of the continuation theorem of coincidence degree theory, existence criteria are established for the existence of periodic solutions and some previous results are extended. 展开更多
关键词 functional differential equation periodic solution coincidence degree
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Adaptive multi-step piecewise interpolation reproducing kernel method for solving the nonlinear time-fractional partial differential equation arising from financial economics 被引量:1
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作者 杜明婧 孙宝军 凯歌 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第3期53-57,共5页
This paper is aimed at solving the nonlinear time-fractional partial differential equation with two small parameters arising from option pricing model in financial economics.The traditional reproducing kernel(RK)metho... This paper is aimed at solving the nonlinear time-fractional partial differential equation with two small parameters arising from option pricing model in financial economics.The traditional reproducing kernel(RK)method which deals with this problem is very troublesome.This paper proposes a new method by adaptive multi-step piecewise interpolation reproducing kernel(AMPIRK)method for the first time.This method has three obvious advantages which are as follows.Firstly,the piecewise number is reduced.Secondly,the calculation accuracy is improved.Finally,the waste time caused by too many fragments is avoided.Then four numerical examples show that this new method has a higher precision and it is a more timesaving numerical method than the others.The research in this paper provides a powerful mathematical tool for solving time-fractional option pricing model which will play an important role in financial economics. 展开更多
关键词 time-fractional partial differential equation adaptive multi-step reproducing kernel method method numerical solution
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The Global Solutions of Impulsive Retarded Functional Differential Equations
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作者 王儒智 孙建安 《Chinese Quarterly Journal of Mathematics》 CSCD 2001年第3期94-99,共6页
In this paper, we present some results on the existence of the golbal solutions of nonlinear impulsive retarded functional differential equations.
关键词 Fréchet spaces Tychonoff fixed point Theorem impulsive retarded functional differential equations
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The Jaffa Transform for Hessian Matrix Systems and the Laplace Equation
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作者 Daniel A. Jaffa 《Journal of Applied Mathematics and Physics》 2024年第1期98-125,共28页
Hessian matrices are square matrices consisting of all possible combinations of second partial derivatives of a scalar-valued initial function. As such, Hessian matrices may be treated as elementary matrix systems of ... Hessian matrices are square matrices consisting of all possible combinations of second partial derivatives of a scalar-valued initial function. As such, Hessian matrices may be treated as elementary matrix systems of linear second-order partial differential equations. This paper discusses the Hessian and its applications in optimization, and then proceeds to introduce and derive the notion of the Jaffa Transform, a new linear operator that directly maps a Hessian square matrix space to the initial corresponding scalar field in nth dimensional Euclidean space. The Jaffa Transform is examined, including the properties of the operator, the transform of notable matrices, and the existence of an inverse Jaffa Transform, which is, by definition, the Hessian matrix operator. The Laplace equation is then noted and investigated, particularly, the relation of the Laplace equation to Poisson’s equation, and the theoretical applications and correlations of harmonic functions to Hessian matrices. The paper concludes by introducing and explicating the Jaffa Theorem, a principle that declares the existence of harmonic Jaffa Transforms, which are, essentially, Jaffa Transform solutions to the Laplace partial differential equation. 展开更多
关键词 Hessian Matrices Jacobian Matrices Laplace equation Linear partial differential equations systems of partial differential equations Harmonic Functions Incompressible and Irrotational Fluid Mechanics
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