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<i>L</i>-Stable Block Hybrid Second Derivative Algorithm for Parabolic Partial Differential Equations
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作者 Fidele Fouogang Ngwane Samuel Nemsefor Jator 《American Journal of Computational Mathematics》 2014年第2期87-92,共6页
An L-stable block method based on hybrid second derivative algorithm (BHSDA) is provided by a continuous second derivative method that is defined for all values of the independent variable and applied to parabolic par... An L-stable block method based on hybrid second derivative algorithm (BHSDA) is provided by a continuous second derivative method that is defined for all values of the independent variable and applied to parabolic partial differential equations (PDEs). The use of the BHSDA to solve PDEs is facilitated by the method of lines which involves making an approximation to the space derivatives, and hence reducing the problem to that of solving a time-dependent system of first order initial value ordinary differential equations. The stability properties of the method is examined and some numerical results presented. 展开更多
关键词 HYBRID Second DERIVATIVE Method Off-Step Point parabolic partial differential equations
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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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THE HIGH ACCURACY EXPLICIT DIFFERENCE SCHEME FOR SOLVING PARABOLIC EQUATIONS 3-DIMENSION
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作者 孙鸿烈 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1999年第7期88-93,共6页
In this paper, an explicit three_level symmetrical differencing scheme with parameters for solving parabolic partial differential equation of three_dimension will be considered. The stability condition and local trunc... In this paper, an explicit three_level symmetrical differencing scheme with parameters for solving parabolic partial differential equation of three_dimension will be considered. The stability condition and local truncation error for the scheme are r<1/2 and O( Δ t 2+ Δ x 4+ Δ y 4+ Δ z 4) ,respectively. 展开更多
关键词 parabolic partial differential equation of three_dimension implicit difference scheme explicit difference scheme local truncation error absolutely stable condition stable
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A SINGULAR PERTURBATION PROBLEM FOR PERIODIC BOUNDARY PARTIAL DIFFERENTIAL EQUATION
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作者 林鹏程 江本铦 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1991年第3期281-290,共10页
In this paper, we consider a singular perturbation elliptic-parabolic partial differential equation for periodic boundary value problem, and construct a difference scheme. Using the method of decomposing the singular ... In this paper, we consider a singular perturbation elliptic-parabolic partial differential equation for periodic boundary value problem, and construct a difference scheme. Using the method of decomposing the singular term from its solution and combining an asymptotic expansion of the equation, we prove that the scheme constructed by this paper converges uniformly to the solution of its original problem with O(r+h2). 展开更多
关键词 elliptic-parabolic partial differential equation singular perturbation problem periodic boundary difference scheme uniform convergence
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Optimality Conditions and Algorithms for Direct Optimizing the Partial Differential Equations
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作者 Victor K. Tolstykh 《Engineering(科研)》 2012年第7期390-393,共4页
New form of necessary conditions for optimality (NCO) is considered. They can be useful for design the direct infinite- dimensional optimization algorithms for systems described by partial differential equations (PDE)... New form of necessary conditions for optimality (NCO) is considered. They can be useful for design the direct infinite- dimensional optimization algorithms for systems described by partial differential equations (PDE). Appropriate algo-rithms for unconstrained minimizing a functional are considered and tested. To construct the algorithms, new form of NCO is used. Such approach demonstrates fast uniform convergence at optimal solution in infinite-dimensional space. 展开更多
关键词 Optimization GRADIENT Necessary Conditions for OPTIMALITY partial differential equationS Infinite-dimensional Algorithms
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Classification of All Single Traveling Wave Solutions to (3 + 1)-Dimensional Breaking Soliton Equation 被引量:1
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作者 Yang Li 《Journal of Applied Mathematics and Physics》 2014年第4期41-45,共5页
In order to get the exact traveling wave solutions to nonlinear partial differential equation, the complete discrimination system for polynomial and direct integral method are applied to the considered equation. All s... In order to get the exact traveling wave solutions to nonlinear partial differential equation, the complete discrimination system for polynomial and direct integral method are applied to the considered equation. All single traveling wave solutions to the equation can be obtained. As an example, we give the solutions to (3 + 1)-dimensional breaking soliton equation. 展开更多
关键词 The Nonlinear partial differential equation Complete Discrimination System for Polynomial Direct Integral Method TRAVELING Wave Transform (3 + 1)-dimensional BREAKING SOLITON equation
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EFFICIENT NUMERICAL ALGORITHMS FOR THREE-DIMENSIONAL FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS 被引量:3
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作者 Weihua Deng Minghua Chen 《Journal of Computational Mathematics》 SCIE CSCD 2014年第4期371-391,共21页
This paper detailedly discusses the locally one-dimensional numerical methods for ef- ficiently solving the three-dimensional fractional partial differential equations, including fractional advection diffusion equatio... This paper detailedly discusses the locally one-dimensional numerical methods for ef- ficiently solving the three-dimensional fractional partial differential equations, including fractional advection diffusion equation and Riesz fractional diffusion equation. The second order finite difference scheme is used to discretize the space fractional derivative and the Crank-Nicolson procedure to the time derivative. We theoretically prove and numerically verify that the presented numerical methods are unconditionally stable and second order convergent in both space and time directions. In particular, for the Riesz fractional dif- fusion equation, the idea of reducing the splitting error is used to further improve the algorithm, and the unconditional stability and convergency are also strictly proved and numerically verified for the improved scheme. 展开更多
关键词 Fractional partial differential equations Numerical stability Locally one dimensional method Crank-Nicolson procedure Alternating direction implicit method.
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A POSTERIORI ERROR ESTIMATE FOR BOUNDARY CONTROL PROBLEMS GOVERNED BY THE PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS 被引量:3
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作者 Wei Gong Ningning Yan 《Journal of Computational Mathematics》 SCIE CSCD 2009年第1期68-88,共21页
In this paper, we discuss the a posteriori error estimate of the finite element approximation for the boundary control problems governed by the parabolic partial differential equations. Three different a posteriori er... In this paper, we discuss the a posteriori error estimate of the finite element approximation for the boundary control problems governed by the parabolic partial differential equations. Three different a posteriori error estimators are provided for the parabolic boundary control problems with the observations of the distributed state, the boundary state and the final state. It is proven that these estimators are reliable bounds of the finite element approximation errors, which can be used as the indicators of the mesh refinement in adaptive finite element methods. 展开更多
关键词 Boundary control problems Finite element method A posteriori error estimate parabolic partial differential equations.
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OSCILLATION THEOREM TO SYSTEMS OF IMPULSIVE NEUTRAL DELAY PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS 被引量:5
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作者 Luo Liping Ouyang Zigen 《Annals of Differential Equations》 2007年第3期297-303,共7页
In this paper, we study the oscillation of solutions to the systems of impulsive neutral delay parabolic partial differential equations. Under two different boundary conditions, we obtain some sufficient conditions fo... In this paper, we study the oscillation of solutions to the systems of impulsive neutral delay parabolic partial differential equations. Under two different boundary conditions, we obtain some sufficient conditions for oscillation of all solutions to the systems. 展开更多
关键词 IMPULSE neutral type DELAY system of parabolic partial differential equations OSCILLATION
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A Fitted Numerov Method for Singularly Perturbed Parabolic Partial Differential Equation with a Small Negative Shift Arising in Control Theory
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作者 R.Nageshwar Rao P.Pramod Chakravarthy 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2014年第1期23-40,共18页
In this paper,a fitted Numerov method is constructed for a class of singularly perturbed one-dimensional parabolic partial differential equations with a small negative shift in the temporal variable.Similar boundary v... In this paper,a fitted Numerov method is constructed for a class of singularly perturbed one-dimensional parabolic partial differential equations with a small negative shift in the temporal variable.Similar boundary value problems are associated with a furnace used to process a metal sheet in control theory.Here,the study focuses on the effect of shift on the boundary layer behavior of the solution via finite difference approach.When the shift parameter is smaller than the perturbation parameter,the shifted term is expanded in Taylor series and an exponentially fitted tridiagonal finite difference scheme is developed.The proposed finite difference scheme is unconditionally stable.When the shift parameter is larger than the perturbation parameter,a special type of mesh is used for the temporal variable so that the shift lies on the nodal points and an exponentially fitted scheme is developed.This scheme is also unconditionally stable.The applicability of the proposed methods is demonstrated by means of two examples. 展开更多
关键词 Singular perturbations parabolic partial differential equation exponentially fitted method differential-difference equations
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ODE-Based Multistep Schemes for Backward Stochastic Differential Equations
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作者 Shuixin Fang Weidong Zhao 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE CSCD 2023年第4期1053-1086,共34页
In this paper,we explore a new approach to design and analyze numerical schemes for backward stochastic differential equations(BSDEs).By the nonlinear Feynman-Kac formula,we reformulate the BSDE into a pair of referen... In this paper,we explore a new approach to design and analyze numerical schemes for backward stochastic differential equations(BSDEs).By the nonlinear Feynman-Kac formula,we reformulate the BSDE into a pair of reference ordinary differential equations(ODEs),which can be directly discretized by many standard ODE solvers,yielding the corresponding numerical schemes for BSDEs.In particular,by applying strong stability preserving(SSP)time discretizations to the reference ODEs,we can propose new SSP multistep schemes for BSDEs.Theoretical analyses are rigorously performed to prove the consistency,stability and convergency of the proposed SSP multistep schemes.Numerical experiments are further carried out to verify our theoretical results and the capacity of the proposed SSP multistep schemes for solving complex associated problems. 展开更多
关键词 Backward stochastic differential equation parabolic partial differential equation strong stability preserving linear multistep scheme high order discretization
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Zakharov-Rubenchik方程组的格子Boltzmann方法
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作者 宋艺 戴厚平 《湖南城市学院学报(自然科学版)》 CAS 2024年第4期73-78,共6页
Zakharov-Rubenchik方程组常用于描述非线性介质中高、低频波间相互作用的波耦合现象。本文针对该方程组的数值求解问题,构建了一种格子Boltzmann方法的D1Q3演化模型,并利用Chapman-Enskog展开和多尺度分析技术,推导出了各个方向的平衡... Zakharov-Rubenchik方程组常用于描述非线性介质中高、低频波间相互作用的波耦合现象。本文针对该方程组的数值求解问题,构建了一种格子Boltzmann方法的D1Q3演化模型,并利用Chapman-Enskog展开和多尺度分析技术,推导出了各个方向的平衡态分布函数和修正函数的具体表达式,从而将所建的演化模型准确恢复到宏观方程组。最后,通过数值算例证明了该方法的有效性。 展开更多
关键词 一维Zakharov-Rubenchik方程组 格子BOLTZMANN方法 数值求解 非线性偏微分方程
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Adaptive Sparse Grid Discontinuous Galerkin Method:Review and Software Implementation
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作者 Juntao Huang Wei Guo Yingda Cheng 《Communications on Applied Mathematics and Computation》 EI 2024年第1期501-532,共32页
This paper reviews the adaptive sparse grid discontinuous Galerkin(aSG-DG)method for computing high dimensional partial differential equations(PDEs)and its software implementation.The C++software package called AdaM-D... This paper reviews the adaptive sparse grid discontinuous Galerkin(aSG-DG)method for computing high dimensional partial differential equations(PDEs)and its software implementation.The C++software package called AdaM-DG,implementing the aSG-DG method,is available on GitHub at https://github.com/JuntaoHuang/adaptive-multiresolution-DG.The package is capable of treating a large class of high dimensional linear and nonlinear PDEs.We review the essential components of the algorithm and the functionality of the software,including the multiwavelets used,assembling of bilinear operators,fast matrix-vector product for data with hierarchical structures.We further demonstrate the performance of the package by reporting the numerical error and the CPU cost for several benchmark tests,including linear transport equations,wave equations,and Hamilton-Jacobi(HJ)equations. 展开更多
关键词 Adaptive sparse grid Discontinuous Galerkin High dimensional partial differential equation Software development
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OSCILLATION OF SYSTEMS OF IMPULSIVE DELAY PARABOLIC EQUATIONS ABOUT BOUNDARY VALUE PROBLEMS 被引量:9
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作者 Luo Lipng Peng Baiyu Yang Liu 《Annals of Differential Equations》 2007年第4期470-476,共7页
In this paper, oscillation of solutions to a class of impulsive delay parabolic partial differential equations system with higher order Laplace operator is studied. Under two different boundary value conditions, we es... In this paper, oscillation of solutions to a class of impulsive delay parabolic partial differential equations system with higher order Laplace operator is studied. Under two different boundary value conditions, we establish some sufficient criteria with respect to the oscillations of such systems, employing first-order impulsive delay differential inequalities. The results fully reflect the influence action of impulsive and delay in oscillation. 展开更多
关键词 IMPULSE DELAY system of parabolic partial differential equations OSCILLATION higher order Laplace operator
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Difference Approximation of Stochastic Elastic Equation Driven by Infinite Dimensional Noise 被引量:1
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作者 Yinghan Zhang Xiaoyuan Yang Ruisheng Qi 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE CSCD 2016年第1期123-146,共24页
An explicit differencescheme is described,analyzed and tested for numer-ically approximating stochastic elastic equation driven by infinite dimensional noise.The noise processes are approximated by piecewise constant ... An explicit differencescheme is described,analyzed and tested for numer-ically approximating stochastic elastic equation driven by infinite dimensional noise.The noise processes are approximated by piecewise constant random processes and the integral formula of the stochastic elastic equation is approximated by a truncated series.Error analysis of the numerical method yields estimate of convergence rate.The rate of convergence is demonstrated with numerical experiments. 展开更多
关键词 Stochastic partial differential equations difference scheme stochastic elastic equation infinite dimensional noise rate of convergence
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EXISTENCE AND UNIQUENESS OF WEAK SOLUTIONS FOR A NONLINEAR PARABOLIC EQUATION RELATED TO IMAGE ANALYSIS 被引量:1
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作者 Wang Lihe Zhou Shulin 《Journal of Partial Differential Equations》 2006年第2期97-112,共16页
In this paper we establish the existence and uniqueness of weak solutions for the initial-boundary value problem of a nonlinear parabolic partial differential equation, which is related to the Malik-Perona model in im... In this paper we establish the existence and uniqueness of weak solutions for the initial-boundary value problem of a nonlinear parabolic partial differential equation, which is related to the Malik-Perona model in image analysis. 展开更多
关键词 EXISTENCE UNIQUENESS nonlinear parabolic partial differential equations.
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A QUASI-NEWTON METHOD IN INFINITE-DIMENSIONAL SPACES AND ITS APPLICATION FOR SOLVING A PARABOLIC INVERSE PROBLEM
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作者 Wen-huan Yu(Department of Mathematics, Tianjin University, Tianjin 300072, P.R. China.) 《Journal of Computational Mathematics》 SCIE CSCD 1998年第4期305-318,共14页
A Quasi-Newton method in Infinite-dimensional Spaces (QNIS) for solving operator equations is presellted and the convergence of a sequence generated by QNIS is also proved in the paper. Next, we suggest a finite-dimen... A Quasi-Newton method in Infinite-dimensional Spaces (QNIS) for solving operator equations is presellted and the convergence of a sequence generated by QNIS is also proved in the paper. Next, we suggest a finite-dimensional implementation of QNIS and prove that the sequence defined by the finite-dimensional algorithm converges to the root of the original operator equation providing that the later exists and that the Frechet derivative of the governing operator is invertible. Finally, we apply QNIS to an inverse problem for a parabolic differential equation to illustrate the efficiency of the finite-dimensional algorithm. 展开更多
关键词 Quasi-Newton method parabolic differential equation inverse problems in partial differential equations linear and Q-superlinear rates of convergence
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On the speed of convergence of Picard iterations of backward stochastic differential equations
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作者 Martin Hutzenthaler Thomas Kruse Tuan Anh Nguyen 《Probability, Uncertainty and Quantitative Risk》 2022年第2期133-150,共18页
It is a well-established fact in the scientific literature that Picard iterations of backward stochastic differential equations with globally Lipschitz continuous nonlinearities converge at least exponentially fast to... It is a well-established fact in the scientific literature that Picard iterations of backward stochastic differential equations with globally Lipschitz continuous nonlinearities converge at least exponentially fast to the solution.In this paper we prove that this convergence is in fact at least square-root factorially fast.We show for one example that no higher convergence speed is possible in general.Moreover,if the nonlinearity is zindependent,then the convergence is even factorially fast.Thus we reveal a phase transition in the speed of convergence of Picard iterations of backward stochastic differential equations. 展开更多
关键词 Backward stochastic differential equation Picard iteration A priori estimate Semilinear parabolic partial differential equation
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An efficient technique for solving fractional-order diffusion equations arising in oil pollution
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作者 Hardik Patel Trushit Patel Dhiren Pandit 《Journal of Ocean Engineering and Science》 SCIE 2023年第3期217-225,共9页
In this article,non-linear time-fractional diffusion equations are considered to describe oil pollution in the water.The latest technique,fractional reduced differential transform method(FRDTM),is used to ac-quire app... In this article,non-linear time-fractional diffusion equations are considered to describe oil pollution in the water.The latest technique,fractional reduced differential transform method(FRDTM),is used to ac-quire approximate solutions of the time fractional-order diffusion equation and two cases of Allen-Cahn equations.The acquired results are collated with the exact solutions and other results from literature for integer-orderα,which reveal that the proposed method is effective.Hence,FRDTM can be employed to obtain solutions for different types of nonlinear fractional-order IVPs arising in engineering and science. 展开更多
关键词 FRDTM Time-fractional nonlinear partial differential equation Diffusion equation Allen-Cahn(AC)equation parabolic equations
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具连续分布滞量的非线性中立型抛物偏泛函微分方程的振动性 被引量:13
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作者 罗李平 高正晖 欧阳自根 《应用数学》 CSCD 北大核心 2006年第3期651-655,共5页
考虑一类具连续分布滞量的非线性中立型抛物偏泛函微分方程解的振动性,借助Green定理和时滞微分不等式获得了这类方程在Robin,Dirichlet边值条件下所有解振动的若干充分条件.
关键词 非线性 中立型 抛物型偏泛函微分方程 振动性 连续分布滞量
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