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THE REGULARIZED SOLUTION APPROXIMATION OF FORWARD/BACKWARD PROBLEMS FOR A FRACTIONAL PSEUDO-PARABOLIC EQUATION WITH RANDOM NOISE
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作者 狄华斐 容伟杰 《Acta Mathematica Scientia》 SCIE CSCD 2023年第1期324-348,共25页
This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Und... This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method. 展开更多
关键词 regularized solution approximation forward/backward problems fractional Laplacian Gaussian white noise Fourier truncation method
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Monte Carlo simulation on backward steps of single kinesin molecule
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作者 王宏 张勇 +1 位作者 窦硕星 王鹏业 《Chinese Physics B》 SCIE EI CAS CSCD 2008年第4期1513-1517,共5页
Kinesin is a stepping molecular motor travelling along the microtubule. It moves primarily in the plus end direction of the microtubule and occasionally in the minus-end, backward, direction. Recently, the backward st... Kinesin is a stepping molecular motor travelling along the microtubule. It moves primarily in the plus end direction of the microtubule and occasionally in the minus-end, backward, direction. Recently, the backward steps of kinesin under different loads and temperatures start to attract interests, and the relations among them are revealed. This paper aims to theoretically understand these relations observed in experiments. After introducing a backward pathway into the previous model of the ATPase cycle of kinesin movement, the dependence of the backward movement on the load and the temperature is explored through Monte Carlo simulation. Our results agree well with previous experiments. 展开更多
关键词 KINESIN backward steps Monte Carlo ATPase cycle
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Forward-backward热方程差分逼近的直接算法
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作者 叶兴德 《浙江大学学报(理学版)》 CAS CSCD 2002年第2期125-128,共4页
通过利用区域分解技术和并行算法的思想 ,把原问题分解为几个完全独立的子区域上的问题 ,并直接并行求解 ,然后把这些解作适当的线性组合 ,得到原问题的解 .给出了 Forward-
关键词 直接算法 forward-backward热方程 有限差分方法 差分逼近 差分格式 区域分解技术 并行算法
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带驻留时间HMM2的Forward-Backward算法
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作者 杜世平 汪建 《重庆工商大学学报(自然科学版)》 2007年第1期9-11,共3页
讨论了用状态驻留时间来模型化传统HMM2模型,对传统HMM2的状态转移和输出观测值的Markov假设条件作了改进,在新模型的转移概率和输出观测值的概率中加入驻留时间,并在传统HMM2的基础上定义了新模型的前向-后向变量算法,导出了新模型的前... 讨论了用状态驻留时间来模型化传统HMM2模型,对传统HMM2的状态转移和输出观测值的Markov假设条件作了改进,在新模型的转移概率和输出观测值的概率中加入驻留时间,并在传统HMM2的基础上定义了新模型的前向-后向变量算法,导出了新模型的前向-后向算法的迭代公式,以及在给定模型λ的条件下,产生观测序列O的概率计算公式. 展开更多
关键词 二阶隐马尔可夫模型 前向-后向算法 驻留时间
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Forward and backward models for fault diagnosis based on parallel genetic algorithms 被引量:10
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作者 Yi LIU Ying LI +1 位作者 Yi-jia CAO Chuang-xin GUO 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2008年第10期1420-1425,共6页
In this paper, a mathematical model consisting of forward and backward models is built on parallel genetic algorithms (PGAs) for fault diagnosis in a transmission power system. A new method to reduce the scale of faul... In this paper, a mathematical model consisting of forward and backward models is built on parallel genetic algorithms (PGAs) for fault diagnosis in a transmission power system. A new method to reduce the scale of fault sections is developed in the forward model and the message passing interface (MPI) approach is chosen to parallel the genetic algorithms by global sin-gle-population master-slave method (GPGAs). The proposed approach is applied to a sample system consisting of 28 sections, 84 protective relays and 40 circuit breakers. Simulation results show that the new model based on GPGAs can achieve very fast computation in online applications of large-scale power systems. 展开更多
关键词 forward and backward models Fault diagnosis Global single-population master-slave genetic algorithms (GPGAs) Parallel computation
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Nonhomogeneous(H,Q)-Process:The Backward and Forward Equations
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作者 陈柳鑫 李俊平 《Journal of Southeast University(English Edition)》 EI CAS 2002年第2期180-183,共4页
As for the backward and forward equation of nonhomogeneous(H, Q) -processes,we proof them in a new way. On the base of that, this paper gives the direct computational formalfor one dimensional distribution of the nonh... As for the backward and forward equation of nonhomogeneous(H, Q) -processes,we proof them in a new way. On the base of that, this paper gives the direct computational formalfor one dimensional distribution of the nonhomogeneous(H, Q) -process. 展开更多
关键词 nonhomogeneous(H Q)-process backward and forward equations one-dimensional distribution
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Determination of the Backward Predictability Limit and Its Relationship with the Forward Predictability Limit 被引量:1
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作者 Xuan LI Ruiqiang DING Jianping LI 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2019年第6期669-677,共9页
In this work, two types of predictability are proposed—forward and backward predictability—and then applied in the nonlinear local Lyapunov exponent approach to the Lorenz63 and Lorenz96 models to quantitatively est... In this work, two types of predictability are proposed—forward and backward predictability—and then applied in the nonlinear local Lyapunov exponent approach to the Lorenz63 and Lorenz96 models to quantitatively estimate the local forward and backward predictability limits of states in phase space. The forward predictability mainly focuses on the forward evolution of initial errors superposed on the initial state over time, while the backward predictability is mainly concerned with when the given state can be predicted before this state happens. From the results, there is a negative correlation between the local forward and backward predictability limits. That is, the forward predictability limits are higher when the backward predictability limits are lower, and vice versa. We also find that the sum of forward and backward predictability limits of each state tends to fluctuate around the average value of sums of the forward and backward predictability limits of sufficient states.Furthermore, the average value is constant when the states are sufficient. For different chaotic systems, the average value is dependent on the chaotic systems and more complex chaotic systems get a lower average value. For a single chaotic system,the average value depends on the magnitude of initial perturbations. The average values decrease as the magnitudes of initial perturbations increase. 展开更多
关键词 nonlinear local LYAPUNOV EXPONENT forward and backward PREDICTABILITY LIMIT negative correlation average value
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A Step Forward toward Effectively Using Hyperspectral IR Sounding Information in NWP 被引量:5
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作者 Jun LI Wei HAN 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2017年第11期1263-1264,共2页
Satellite-based atmospheric sounding measurements with high spectral resolution or from hyperspectral infrared (IR) sounders are important global observations for improving weather forecasts through assimilating the... Satellite-based atmospheric sounding measurements with high spectral resolution or from hyperspectral infrared (IR) sounders are important global observations for improving weather forecasts through assimilating them into operational numerical weather prediction (NWP) systems. 展开更多
关键词 In A step forward toward Effectively Using Hyperspectral IR Sounding Information in NWP
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The Maximum Principle for Fully Coupled Forward-backward Stochastic Control System 被引量:14
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作者 SHI Jing-Tao WU Zhen 《自动化学报》 EI CSCD 北大核心 2006年第2期161-169,共9页
The maximum principle for fully coupled forward-backward stochastic control system in the global form is proved, under the assumption that the forward diffusion coefficient does not contain the control variable, but t... The maximum principle for fully coupled forward-backward stochastic control system in the global form is proved, under the assumption that the forward diffusion coefficient does not contain the control variable, but the control domain is not necessarily convex. 展开更多
关键词 最大原理 随机控制系统 毛刺变异 扩散系数
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Solution of scattering from rough surface with a 2D target above it by a hybrid method based on the reciprocity theorem and the forward-backward method 被引量:4
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作者 王运华 张彦敏 +1 位作者 贺明霞 郭立新 《Chinese Physics B》 SCIE EI CAS CSCD 2008年第10期3696-3703,共8页
This paper proposes a hybrid method based on the forward-backward method (FBM) and the reciprocity theorem (RT) for evaluating the scattering field from dielectric rough surface with a 2D target above it. Here, th... This paper proposes a hybrid method based on the forward-backward method (FBM) and the reciprocity theorem (RT) for evaluating the scattering field from dielectric rough surface with a 2D target above it. Here, the equivalent electric/magnetic current densities on the rough surface as well as the scattering field from it are numerically calculated by FBM, and the scattered field from the isolated target is obtained utilizing the method of moments (MOM). Meanwhile, the rescattered coupling interactions between the target and the surface are evaluated employing the combination of FBM and RT. Our hybrid method is first validated by available MOM results. Then, the functional dependences of bistatic and monostatic scattering from the target above rough surface upon the target altitude, incident and scattering angles are numerically simulated and discussed. This study presents a numerical description for the scattering mechanism associated with rescattered coupling interactions between a target and an underlying randomly rough surface. 展开更多
关键词 forward-backward method reciprocity theorem 2D target rough surface SCATTERING
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Forward-backward multiplicity correlations 4.5 A GeV/c ^16O-emulsion interactions 被引量:4
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作者 张东海 赵惠华 +5 位作者 刘芳 何春乐 贾会明 李雷琴 李振宇 李俊生 《Chinese Physics B》 SCIE EI CAS CSCD 2006年第9期1987-1995,共9页
A detailed study of the mechanisms of the emissions of pions and protons in the forward and backward hemispheres in 4.5 A GeV/c oxygen-emulsion interactions has been carried out. The correlations between the multiplic... A detailed study of the mechanisms of the emissions of pions and protons in the forward and backward hemispheres in 4.5 A GeV/c oxygen-emulsion interactions has been carried out. The correlations between the multiplicities of secondary charged particles in the backward and forward hemispheres are investigated. 展开更多
关键词 relativistic heavy-ion collision backward-forward correlation nuclear emulsion
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Numerical simulation of flow separation over a backward-facing step with high Reynolds number 被引量:6
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作者 Fang-fang Wang Shi-qiang Wu Sen-lin Zhu 《Water Science and Engineering》 EI CAS CSCD 2019年第2期145-154,共10页
Large eddy simulation (LES) explicitly calculates the large-scale vortex field and parameterizes the small-scale vortices.In this study,LES and κ-ε models were developed for a specific geometrical configuration of b... Large eddy simulation (LES) explicitly calculates the large-scale vortex field and parameterizes the small-scale vortices.In this study,LES and κ-ε models were developed for a specific geometrical configuration of backward-facing step (BFS).The simulation results were validated with particle image velocimetry (PIV) measurements and direct numerical simulation (DNS).This LES simulation was carried out with a Reynolds number of 9000 in a pressurized water tunnel with an expansion ratio of 2.00.The results indicate that the LES model can reveal largescale vortex motion although with a larger grid-cell size.However,the LES model tends to overestimate the top wall separation and the Reynolds stress components for the BFS flow simulation without a sufficiently fine grid.Overall,LES is a potential tool for simulating separated flow controlled by large-scale vortices. 展开更多
关键词 Large EDDY SIMULATION κ-ε model backward-facing step Direct numerical SIMULATION Large-scale VORTICES Particle image VELOCIMETRY
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FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH STOPPING TIME 被引量:2
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作者 吴臻 《Acta Mathematica Scientia》 SCIE CSCD 2004年第1期91-99,共9页
The existence and uniqueness results of fully coupled forward-backward stochastic differential equations with stopping time (unbounded) is obtained. One kind of comparison theorem for this kind of equations is also pr... The existence and uniqueness results of fully coupled forward-backward stochastic differential equations with stopping time (unbounded) is obtained. One kind of comparison theorem for this kind of equations is also proved. 展开更多
关键词 forward-backward stochastic differential equations stopping time comparison theorem
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Solutions to general forward-backward doubly stochastic differential equations 被引量:1
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作者 朱庆峰 石玉峰 宫献军 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2009年第4期517-526,共10页
A general type of forward-backward doubly stochastic differential equations (FBDSDEs) is studied. It extends many important equations that have been well studied, including stochastic Hamiltonian systems. Under some... A general type of forward-backward doubly stochastic differential equations (FBDSDEs) is studied. It extends many important equations that have been well studied, including stochastic Hamiltonian systems. Under some much weaker monotonicity assumptions, the existence and uniqueness of measurable solutions are established with a incthod of continuation. Furthermore, the continuity and differentiability of the solutions to FBDSDEs depending on parameters is discussed. 展开更多
关键词 forward-backward doubly stochastic differential equations method of con-tinuation H-monotone
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EXPERIMENTAL INVESTIGATION ON THE TURBULENT COHERENT STRUCTURES OF LAMINAR SEPARATION FLOW OVER A BACKWARD FACING STEP
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作者 Wang Jinjun Lian Qixiang Lan Shilong(Fluid Mechanics Institute, Beijing University of Aeronautics and Astronautics, Beijing, China, 100083) 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 1996年第3期175-181,共7页
The experimental investigation is conducted with LDV and hydrogen bubble technique in water flow. The shear layer thickness. the vorticity thickness. the maximulll value of turbulence intensities. the turbulent coher... The experimental investigation is conducted with LDV and hydrogen bubble technique in water flow. The shear layer thickness. the vorticity thickness. the maximulll value of turbulence intensities. the turbulent coherent structure. the variations of wall shear stress and the boundary layer shape factor are obtained. In the redevelopment region. the detailed analysis is first made for the streak structures in the near wall region and the turbulent boundary layer is formed at (x-xr) / h = 20. 展开更多
关键词 backward facing steps laminar boundary layer separated flow turbulent boundary layer reattached flow
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A Mean-Field Stochastic Maximum Principle for Optimal Control of Forward-Backward Stochastic Differential Equations with Jumps via Malliavin Calculus 被引量:1
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作者 Qing Zhou Yong Ren 《Journal of Applied Mathematics and Physics》 2018年第1期138-154,共17页
This paper considers a mean-field type stochastic control problem where the dynamics is governed by a forward and backward stochastic differential equation (SDE) driven by Lévy processes and the information avail... This paper considers a mean-field type stochastic control problem where the dynamics is governed by a forward and backward stochastic differential equation (SDE) driven by Lévy processes and the information available to the controller is possibly less than the overall information. All the system coefficients and the objective performance functional are allowed to be random, possibly non-Markovian. Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed. 展开更多
关键词 Malliavin CALCULUS Maximum PRINCIPLE forward-backward Stochastic Differential Equations MEAN-FIELD Type JUMP Diffusion Partial Information
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Effect of Richardson number on entropy generation over backward facing step
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作者 陈胜 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2012年第11期1431-1440,共10页
The flow over a backward facing step (BFS) has been taken as a useful proto- type to investigate intrinsic mechanisms of separated flow with heat transfer. However, to date, the open literature on the effect of Rich... The flow over a backward facing step (BFS) has been taken as a useful proto- type to investigate intrinsic mechanisms of separated flow with heat transfer. However, to date, the open literature on the effect of Richardson number on entropy generation over the BFS is absent yet, although the flow pattern and heat transfer characteristic both will receive significant influence caused by the variation of Richardson number in many prac- tical applications, such as in microelectromechanical systems and aerocrafts. The effect of Richardson number on entropy generation in the BFS flow is reported in this paper for the first time. The entropy generation analysis is conducted through numerically solving the entropy generation equation. The velocity and temperature, which are the inputs of the entropy generation equation, are evaluated by the lattice Boltzmann method. It is found that the distributions of local entropy generation number and Bejan number are significantly influenced by the variation of Richardson number. The total entropy gen- eration number is a monotonic decreasing function of Richardson number, whereas the average Bejan number is a monotonic increasing function of Richardson number. 展开更多
关键词 entropy generation backward facing step Richardson number latticeBoltzmann method
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Effects of Baffle on Entropy Generation in Separated Convection Flow Adjacent to Inclined Backward-Facing Step
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作者 Asad Bahrami Seyyed Abdolreza Gandjalikhan Nassab Maliheh Hashemipour 《Journal of Electronics Cooling and Thermal Control》 2012年第4期53-61,共9页
Numerical simulations of a two-dimensional laminar forced convection flow adjacent to inclined backward-facing step in a rectangular duct are presented to examine effects of baffle on flow, heat transfer and entropy g... Numerical simulations of a two-dimensional laminar forced convection flow adjacent to inclined backward-facing step in a rectangular duct are presented to examine effects of baffle on flow, heat transfer and entropy generation distributions. The main aim of using baffles is to enhance the value of convection coefficient on the bottom wall. But the useful energy can be destroyed due to intrinsic irreversibilities in the flow by the baffle. In the present work, the amount of energy loss is estimated by the computation of entropy generation. The values of velocity and temperature which are the inputs of the entropy generation equation are obtained by the numerical solution of momentum and energy equations with blocked-off method using computational fluid dynamic technique. Discretized forms of the governing equations in the (x, y) plane are obtained by the control volume method and solved using the SIMPLE algorithm. Numerical expressions, in terms of Nusselt number, entropy generation number, Bejan number and coefficient of friction are derived in dimensionless form. Results show that although a baffle mounted onto the upper wall increases the magnitude of Nusselts number on the bottom wall, but a considerable increase in the amount of entropy generation number takes place because of this technique. For validation, the numerical results for the Nusselt number and entropy generation number are compared with theoretical findings by other investigators and reasonable agreement is found. 展开更多
关键词 ENTROPY Generation Inclined backward step BAFFLE CONVECTION Flow
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求解双层凸优化问题的Forward-Backward分裂算法
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作者 李明川 叶明露 《西华师范大学学报(自然科学版)》 2020年第1期46-51,共6页
Forward-Backward分裂算法是求解极大单调算子和问题以及极小化具有可分结构的凸函数和问题的有效算法。本文利用该算法在Hilbert空间中构造出了求解双层优化问题的分裂算法。与已有文献相比,所提算法不仅在参数的选取上更加灵活,而且... Forward-Backward分裂算法是求解极大单调算子和问题以及极小化具有可分结构的凸函数和问题的有效算法。本文利用该算法在Hilbert空间中构造出了求解双层优化问题的分裂算法。与已有文献相比,所提算法不仅在参数的选取上更加灵活,而且本文还证明了该算法生成的点列能收敛到双层优化问题的解。 展开更多
关键词 极大单调算子 双层优化 非扩张映射 forward-backward算法 弱收敛列
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An Adaptive Time-Step Backward Differentiation Algorithm to Solve Stiff Ordinary Differential Equations: Application to Solve Activated Sludge Models 被引量:2
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作者 Jamal Alikhani Bahareh Shoghli +1 位作者 Ujjal Kumar Bhowmik Arash Massoudieh 《American Journal of Computational Mathematics》 2016年第4期298-312,共15页
A backward differentiation formula (BDF) has been shown to be an effective way to solve a system of ordinary differential equations (ODEs) that have some degree of stiffness. However, sometimes, due to high-frequency ... A backward differentiation formula (BDF) has been shown to be an effective way to solve a system of ordinary differential equations (ODEs) that have some degree of stiffness. However, sometimes, due to high-frequency variations in the external time series of boundary conditions, a small time-step is required to solve the ODE system throughout the entire simulation period, which can lead to a high computational cost, slower response, and need for more memory resources. One possible strategy to overcome this problem is to dynamically adjust the time-step with respect to the system’s stiffness. Therefore, small time-steps can be applied when needed, and larger time-steps can be used when allowable. This paper presents a new algorithm for adjusting the dynamic time-step based on a BDF discretization method. The parameters used to dynamically adjust the size of the time-step can be optimally specified to result in a minimum computation time and reasonable accuracy for a particular case of ODEs. The proposed algorithm was applied to solve the system of ODEs obtained from an activated sludge model (ASM) for biological wastewater treatment processes. The algorithm was tested for various solver parameters, and the optimum set of three adjustable parameters that represented minimum computation time was identified. In addition, the accuracy of the algorithm was evaluated for various sets of solver parameters. 展开更多
关键词 Adaptive Time-step backward Differentiation Formula Activated Sludge Model Ordinary Differential Equation Stiffness Computation Time
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