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Mathematics and Statistics Faculty Research & Creative Works

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Full-Text Articles in Statistics and Probability

Asymptotic Stability Of Solitary Waves For The 1d Nls With An Attractive Delta Potential, Satoshi Masaki, Jason Murphy, Jun Ichi Segata Jun 2023

Asymptotic Stability Of Solitary Waves For The 1d Nls With An Attractive Delta Potential, Satoshi Masaki, Jason Murphy, Jun Ichi Segata

Mathematics and Statistics Faculty Research & Creative Works

We Consider the One-Dimensional Nonlinear Schrödinger Equation with an Attractive Delta Potential and Mass-Supercritical Nonlinearity. This Equation Admits a One-Parameter Family of Solitary Wave Solutions in Both the Focusing and Defocusing Cases. We Establish Asymptotic Stability for All Solitary Waves Satisfying a Suitable Spectral Condition, Namely, that the Linearized Operator Around the Solitary Wave Has a Two-Dimensional Generalized Kernel and No Other Eigenvalues or Resonances. in Particular, We Extend Our Previous Result [35] Beyond the Regime of Small Solitary Waves and Extend the Results of [19, 29] from Orbital to Asymptotic Stability for a Suitable Family of Solitary Waves.

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Fractal Newton Methods, Ali Akgül, David E. Grow May 2023

Fractal Newton Methods, Ali Akgül, David E. Grow

Mathematics and Statistics Faculty Research & Creative Works

We introduce fractal Newton methods for solving (Formula presented.) that generalize and improve the classical Newton method. We compare the theoretical efficacy of the classical and fractal Newton methods and illustrate the theory with examples.

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Fully Decoupled Energy-Stable Numerical Schemes For Two-Phase Coupled Porous Media And Free Flow With Different Densities And Viscosities, Yali Gao, Xiaoming He, Tao Lin, Yanping Lin May 2023

Fully Decoupled Energy-Stable Numerical Schemes For Two-Phase Coupled Porous Media And Free Flow With Different Densities And Viscosities, Yali Gao, Xiaoming He, Tao Lin, Yanping Lin

Mathematics and Statistics Faculty Research & Creative Works

In this article, we consider a phase field model with different densities and viscosities for the coupled two-phase porous media flow and two-phase free flow, as well as the corresponding numerical simulation. This model consists of three parts: a Cahn-Hilliard-Darcy system with different densities/viscosities describing the porous media flow in matrix, a Cahn-illiard-Navier-Stokes system with different densities/viscosities describing the free fluid in conduit, and seven interface conditions coupling the flows in the matrix and the conduit. Based on the separate Cahn-Hilliard equations in the porous media region and the free flow region, a weak formulation is proposed to incorporate the …

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An Integer Garch Model For A Poisson Process With Time-Varying Zero-Inflation, Isuru Panduka Ratnayake, V. A. Samaranayake May 2023

An Integer Garch Model For A Poisson Process With Time-Varying Zero-Inflation, Isuru Panduka Ratnayake, V. A. Samaranayake

Mathematics and Statistics Faculty Research & Creative Works

A serially dependent Poisson process with time-varying zero-inflation is proposed. Such formulations have the potential to model count data time series arising from phenomena such as infectious diseases that ebb and flow over time. The model assumes that the intensity of the Poisson process evolves according to a generalized autoregressive conditional heteroscedastic (GARCH) formulation and allows the zero-inflation parameter to vary over time and be governed by a deterministic function or by an exogenous variable. Both the expectation maximization (EM) and the maximum likelihood estimation (MLE) approaches are presented as possible estimation methods. A simulation study shows that both parameter …

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A New Approach To Proper Orthogonal Decomposition With Difference Quotients, Sarah Locke Eskew, John R. Singler Apr 2023

A New Approach To Proper Orthogonal Decomposition With Difference Quotients, Sarah Locke Eskew, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

In a Recent Work (Koc Et Al., SIAM J. Numer. Anal. 59(4), 2163–2196, 2021), the Authors Showed that Including Difference Quotients (DQs) is Necessary in Order to Prove Optimal Pointwise in Time Error Bounds for Proper Orthogonal Decomposition (POD) Reduced Order Models of the Heat Equation. in This Work, We Introduce a New Approach to Including DQs in the POD Procedure. Instead of Computing the POD Modes using All of the Snapshot Data and DQs, We Only Use the First Snapshot Along with All of the DQs and Special POD Weights. We Show that This Approach Retains All of the …

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Rank-Based Inference For Survey Sampling Data, Akim Adekpedjou, Huybrechts F. Bindele Apr 2023

Rank-Based Inference For Survey Sampling Data, Akim Adekpedjou, Huybrechts F. Bindele

Mathematics and Statistics Faculty Research & Creative Works

For regression models where data are obtained from sampling surveies, the statistical analysis is often based on approaches that are either non-robust or inefficient. The handling of survey data requires more appropriate techniques, as the classical methods usually result in biased and inefficient estimates of the underlying model parameters. This article is concerned with the development of a new approach of obtaining robust and efficient estimates of regression model parameters when dealing with survey sampling data. Asymptotic properties of such estimators are established under mild regularity conditions. To demonstrate the performance of the proposed method, Monte Carlo simulation experiments are …

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Dynamic Equations, Control Problems On Time Scales, And Chaotic Systems, Martin Bohner Mar 2023

Dynamic Equations, Control Problems On Time Scales, And Chaotic Systems, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

The unification of integral and differential calculus with the calculus of finite differences has been rendered possible by providing a formal structure to study hybrid discrete-continuous dynamical systems besides offering applications in diverse fields that require simultaneous modeling of discrete and continuous data concerning dynamic equations on time scales. Therefore, the theory of time scales provides a unification between the calculus of the theory of difference equations with the theory of differential equations. In addition, it has become possible to examine diverse application problems more precisely by the use of dynamical systems on time scales whose calculus is made up …

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Error Analysis Of A Fully Discrete Projection Method For Magnetohydrodynamic System, Qianqian Ding, Xiaoming He, Xiaonian Long, Shipeng Mao Mar 2023

Error Analysis Of A Fully Discrete Projection Method For Magnetohydrodynamic System, Qianqian Ding, Xiaoming He, Xiaonian Long, Shipeng Mao

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we develop and analyze a finite element projection method for magnetohydrodynamics equations in Lipschitz domain. A fully discrete scheme based on Euler semi-implicit method is proposed, in which continuous elements are used to approximate the Navier–Stokes equations and H(curl) conforming Nédélec edge elements are used to approximate the magnetic equation. One key point of the projection method is to be compatible with two different spaces for calculating velocity, which leads one to obtain the pressure by solving a Poisson equation. The results show that the proposed projection scheme meets a discrete energy stability. In addition, with the …

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Error Analysis Of A Fully Discrete Projection Method For Magnetohydrodynamic System, Qianqian Ding, Xiaoming He, Xiaonian Long, Shipeng Mao Mar 2023

Error Analysis Of A Fully Discrete Projection Method For Magnetohydrodynamic System, Qianqian Ding, Xiaoming He, Xiaonian Long, Shipeng Mao

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we develop and analyze a finite element projection method for magnetohydrodynamics equations in Lipschitz domain. A fully discrete scheme based on Euler semi-implicit method is proposed, in which continuous elements are used to approximate the Navier–Stokes equations and H(curl) conforming Nédélec edge elements are used to approximate the magnetic equation. One key point of the projection method is to be compatible with two different spaces for calculating velocity, which leads one to obtain the pressure by solving a Poisson equation. The results show that the proposed projection scheme meets a discrete energy stability. In addition, with the …

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A New Global Divergence Free And Pressure-Robust Hdg Method For Tangential Boundary Control Of Stokes Equations, Gang Chen, Wei Gong, Mariano Mateos, John R. Singler, Yangwen Zhang Feb 2023

A New Global Divergence Free And Pressure-Robust Hdg Method For Tangential Boundary Control Of Stokes Equations, Gang Chen, Wei Gong, Mariano Mateos, John R. Singler, Yangwen Zhang

Mathematics and Statistics Faculty Research & Creative Works

In Gong et al. (2020), we proposed an HDG method to approximate the solution of a tangential boundary control problem for the Stokes equations and obtained an optimal convergence rate for the optimal control that reflects its global regularity. However, the error estimates depend on the pressure, and the velocity is not divergence free. The importance of pressure-robust numerical methods for fluids was addressed by John et al. (2017). In this work, we devise a new HDG method to approximate the solution of the Stokes tangential boundary control problem; the HDG method is also of independent interest for solving the …

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A New Global Divergence Free And Pressure-Robust Hdg Method For Tangential Boundary Control Of Stokes Equations, Gang Chen, Wei Gong, Mariano Mateos, John R. Singler, Yangwen Zhang Feb 2023

A New Global Divergence Free And Pressure-Robust Hdg Method For Tangential Boundary Control Of Stokes Equations, Gang Chen, Wei Gong, Mariano Mateos, John R. Singler, Yangwen Zhang

Mathematics and Statistics Faculty Research & Creative Works

In Gong et al. (2020), we proposed an HDG method to approximate the solution of a tangential boundary control problem for the Stokes equations and obtained an optimal convergence rate for the optimal control that reflects its global regularity. However, the error estimates depend on the pressure, and the velocity is not divergence free. The importance of pressure-robust numerical methods for fluids was addressed by John et al. (2017). In this work, we devise a new HDG method to approximate the solution of the Stokes tangential boundary control problem; the HDG method is also of independent interest for solving the …

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Post-Quantum Hermite-Jensen-Mercer Inequalities, Martin Bohner, Hüseyin Budak, Hasan Kara Feb 2023

Post-Quantum Hermite-Jensen-Mercer Inequalities, Martin Bohner, Hüseyin Budak, Hasan Kara

Mathematics and Statistics Faculty Research & Creative Works

The Jensen-Mercer inequality, which is well known in the literature, has an important place in mathematics and related disciplines. In this work, we obtain the Hermite-Jensen-Mercer inequality for post-quantum integrals by utilizing Jensen-Mercer inequalities. Then we investigate the connections between our results and those in earlier works. Moreover, we give some examples to illustrate our main results. This is the first paper about Hermite-Jensen-Mercer inequalities for post-quantum integrals.

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Inequalities For Interval-Valued Riemann Diamond-Alpha Integrals, Martin Bohner, Linh Nguyen, Baruch Schneider, Tri Truong Jan 2023

Inequalities For Interval-Valued Riemann Diamond-Alpha Integrals, Martin Bohner, Linh Nguyen, Baruch Schneider, Tri Truong

Mathematics and Statistics Faculty Research & Creative Works

We propose the concept of Riemann diamond-alpha integrals for time scales interval-valued functions. We first give the definition and some properties of the interval Riemann diamond-alpha integral that are naturally investigated as an extension of interval Riemann nabla and delta integrals. With the help of the interval Riemann diamond-alpha integral, we present interval variants of Jensen inequalities for convex and concave interval-valued functions on an arbitrary time scale. Moreover, diamond alpha Hölder's and Minkowski's interval inequalities are proved. Also, several numerical examples are provided in order to illustrate our main results.

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Oscillation Of Second-Order Half-Linear Neutral Noncanonical Dynamic Equations, Martin Bohner, Hassan El-Morshedy, Said Grace, Irena Jadlovská Jan 2023

Oscillation Of Second-Order Half-Linear Neutral Noncanonical Dynamic Equations, Martin Bohner, Hassan El-Morshedy, Said Grace, Irena Jadlovská

Mathematics and Statistics Faculty Research & Creative Works

In This Paper, We Shall Establish Some New Criteria for the Oscillation of Certain Second-Order Noncanonical Dynamic Equations with a Sublinear Neutral Term. This Task is Accomplished by Reducing the Involved Nonlinear Dynamic Equation to a Second-Order Linear Dynamic Inequality. We Also Establish Some New Oscillation Theorems Involving Certain Integral Conditions. Three Examples, Illustrating Our Results, Are Presented. Our Results Generalize Results for Corresponding Differential and Difference Equations.

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Trilinear Immersed-Finite-Element Method For Three-Dimensional Anisotropic Interface Problems In Plasma Thrusters, Yajie Han, Guangqing Xia, Chang Lu, Xiaoming He Jan 2023

Trilinear Immersed-Finite-Element Method For Three-Dimensional Anisotropic Interface Problems In Plasma Thrusters, Yajie Han, Guangqing Xia, Chang Lu, Xiaoming He

Mathematics and Statistics Faculty Research & Creative Works

Accurately solving the anisotropic interface problem is one of the difficulties in aerospace plasma applications. Based on cubic Cartesian meshes, this paper develops a trilinear nonhomogeneous immersed finite element (IFE) method for solving the complex anisotropic 3D elliptic interface model with nonhomogeneous flux jump. Compared with the existing 3D linear IFE spaces based on tetrahedron meshes, the newly designed trilinear IFE space for the target model simplifies the mesh generation, significantly reduces the number of mesh elements and interface elements, provides much more convenient and efficient ways for finding the intersections between interfaces and mesh edges, and decreases the errors. …

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Variable-Dependent Partial Dimension Reduction, Lu Li, Kai Tan, Xuerong Meggie Wen, Zhou Yu Jan 2023

Variable-Dependent Partial Dimension Reduction, Lu Li, Kai Tan, Xuerong Meggie Wen, Zhou Yu

Mathematics and Statistics Faculty Research & Creative Works

Sufficient dimension reduction reduces the dimension of a regression model without loss of information by replacing the original predictor with its lower-dimensional linear combinations. Partial (sufficient) dimension reduction arises when the predictors naturally fall into two sets X and W, and pursues a partial dimension reduction of X. Though partial dimension reduction is a very general problem, only very few research results are available when W is continuous. To the best of our knowledge, none can deal with the situation where the reduced lower-dimensional subspace of X varies with W. To address such issue, we in this paper propose a …

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Variable-Dependent Partial Dimension Reduction, Lu Li, Kai Tan, Xuerong Meggie Wen, Zhou Yu Jan 2023

Variable-Dependent Partial Dimension Reduction, Lu Li, Kai Tan, Xuerong Meggie Wen, Zhou Yu

Mathematics and Statistics Faculty Research & Creative Works

Sufficient dimension reduction reduces the dimension of a regression model without loss of information by replacing the original predictor with its lower-dimensional linear combinations. Partial (sufficient) dimension reduction arises when the predictors naturally fall into two sets X and W, and pursues a partial dimension reduction of X. Though partial dimension reduction is a very general problem, only very few research results are available when W is continuous. To the best of our knowledge, none can deal with the situation where the reduced lower-dimensional subspace of X varies with W. To address such issue, we in this paper propose a …

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The Generalized Lyapunov Function As Ao’S Potential Function: Existence In Dimensions 1 And 2, Haoyu Wang, Wenqing Hu, Xiaoliang Gan, Ping Ao Jan 2023

The Generalized Lyapunov Function As Ao’S Potential Function: Existence In Dimensions 1 And 2, Haoyu Wang, Wenqing Hu, Xiaoliang Gan, Ping Ao

Mathematics and Statistics Faculty Research & Creative Works

By using Ao's decomposition for stochastic dynamical systems, a new notion of potential function has been introduced by Ao and his collabora-tors recently. We show that this potential function agrees with the generalized Lyapunov function of the deterministic part of the stochastic dynamical sys-tem. We further prove the existence of Ao's potential function in dimensions 1 and 2 via the solution theory of first-order partial differential equations. Our framework reveals the equivalence between Ao's potential function and Lyapunov function, the latter being one of the most significant central notions in dynamical systems. Using this equivalence, our existence proof can also …

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Three Solutions For Discrete Anisotropic Kirchhoff-Type Problems, Martin Bohner, Giuseppe Caristi, Ahmad Ghobadi, Shapour Heidarkhani Jan 2023

Three Solutions For Discrete Anisotropic Kirchhoff-Type Problems, Martin Bohner, Giuseppe Caristi, Ahmad Ghobadi, Shapour Heidarkhani

Mathematics and Statistics Faculty Research & Creative Works

In this article, using critical point theory and variational methods, we investigate the existence of at least three solutions for a class of double eigenvalue discrete anisotropic Kirchhoff-type problems. An example is presented to demonstrate the applicability of our main theoretical findings.

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Second Order, Unconditionally Stable, Linear Ensemble Algorithms For The Magnetohydrodynamics Equations, John Carter, Daozhi Han, Nan Jiang Jan 2023

Second Order, Unconditionally Stable, Linear Ensemble Algorithms For The Magnetohydrodynamics Equations, John Carter, Daozhi Han, Nan Jiang

Mathematics and Statistics Faculty Research & Creative Works

We Propose Two Unconditionally Stable, Linear Ensemble Algorithms with Pre-Computable Shared Coefficient Matrices Across Different Realizations for the Magnetohydrodynamics Equations. the Viscous Terms Are Treated by a Standard Perturbative Discretization. the Nonlinear Terms Are Discretized Fully Explicitly within the Framework of the Generalized Positive Auxiliary Variable Approach (GPAV). Artificial Viscosity Stabilization that Modifies the Kinetic Energy is Introduced to Improve Accuracy of the GPAV Ensemble Methods. Numerical Results Are Presented to Demonstrate the Accuracy and Robustness of the Ensemble Algorithms.

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Predicting Convection Configurations In Coupled Fluid-Porous Systems, Matthew Mccurdy, Nicholas J. Moore, Xiaoming Wang Dec 2022

Predicting Convection Configurations In Coupled Fluid-Porous Systems, Matthew Mccurdy, Nicholas J. Moore, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

A ubiquitous arrangement in nature is a free-flowing fluid coupled to a porous medium, for example a river or lake lying above a porous bed. Depending on the environmental conditions, thermal convection can occur and may be confined to the clear fluid region, forming shallow convection cells, or it can penetrate into the porous medium, forming deep cells. Here, we combine three complementary approaches - linear stability analysis, fully nonlinear numerical simulations and a coarse-grained model - to determine the circumstances that lead to each configuration. the coarse-grained model yields an explicit formula for the transition between deep and shallow …

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Second-Order, Fully Decoupled, Linearized, And Unconditionally Stable Scalar Auxiliary Variable Schemes For Cahn–Hilliard–Darcy System, Yali Gao, Xiaoming He, Yufeng Nie Nov 2022

Second-Order, Fully Decoupled, Linearized, And Unconditionally Stable Scalar Auxiliary Variable Schemes For Cahn–Hilliard–Darcy System, Yali Gao, Xiaoming He, Yufeng Nie

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we establish the fully decoupled numerical methods by utilizing scalar auxiliary variable approach for solving Cahn–Hilliard–Darcy system. We exploit the operator splitting technique to decouple the coupled system and Galerkin finite element method in space to construct the fully discrete formulation. The developed numerical methods have the features of second order accuracy, totally decoupling, linearization, and unconditional energy stability. The unconditionally stability of the two proposed decoupled numerical schemes are rigorously proved. Abundant numerical results are reported to verify the accuracy and effectiveness of proposed numerical methods.

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Conservative Unconditionally Stable Decoupled Numerical Schemes For The Cahn–Hilliard–Navier–Stokes–Darcy–Boussinesq System, Wenbin Chen, Daozhi Han, Xiaoming Wang, Yichao Zhang Nov 2022

Conservative Unconditionally Stable Decoupled Numerical Schemes For The Cahn–Hilliard–Navier–Stokes–Darcy–Boussinesq System, Wenbin Chen, Daozhi Han, Xiaoming Wang, Yichao Zhang

Mathematics and Statistics Faculty Research & Creative Works

We propose two mass and heat energy conservative, unconditionally stable, decoupled numerical algorithms for solving the Cahn–Hilliard–Navier–Stokes–Darcy–Boussinesq system that models thermal convection of two-phase flows in superposed free flow and porous media. The schemes totally decouple the computation of the Cahn–Hilliard equation, the Darcy equations, the heat equation, the Navier–Stokes equations at each time step, and thus significantly reducing the computational cost. We rigorously show that the schemes are conservative and energy-law preserving. Numerical results are presented to demonstrate the accuracy and stability of the algorithms.

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Pattern Selection In The Schnakenberg Equations: From Normal To Anomalous Diffusion, Hatim K. Khudhair, Yanzhi Zhang, Nobuyuki Fukawa Nov 2022

Pattern Selection In The Schnakenberg Equations: From Normal To Anomalous Diffusion, Hatim K. Khudhair, Yanzhi Zhang, Nobuyuki Fukawa

Mathematics and Statistics Faculty Research & Creative Works

Pattern formation in the classical and fractional Schnakenberg equations is studied to understand the nonlocal effects of anomalous diffusion. Starting with linear stability analysis, we find that if the activator and inhibitor have the same diffusion power, the Turing instability space depends only on the ratio of diffusion coefficients (Formula presented.). However, smaller diffusive powers might introduce larger unstable wave numbers with wider band, implying that the patterns may be more chaotic in the fractional cases. We then apply a weakly nonlinear analysis to predict the parameter regimes for spot, stripe, and mixed patterns in the Turing space. Our numerical …

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Numerical Analysis Of A Second Order Ensemble Method For Evolutionary Magnetohydrodynamics Equations At Small Magnetic Reynolds Number, John Carter, Nan Jiang Sep 2022

Numerical Analysis Of A Second Order Ensemble Method For Evolutionary Magnetohydrodynamics Equations At Small Magnetic Reynolds Number, John Carter, Nan Jiang

Mathematics and Statistics Faculty Research & Creative Works

We study a second order ensemble method for fast computation of an ensemble of magnetohydrodynamics flows at small magnetic Reynolds number. Computing an ensemble of flow equations with different input parameters is a common procedure for uncertainty quantification in many engineering applications, for which the computational cost can be prohibitively expensive for nonlinear complex systems. We propose an ensemble algorithm that requires only solving one linear system with multiple right-hands instead of solving multiple different linear systems, which significantly reduces the computational cost and simulation time. Comprehensive stability and error analyses are presented proving conditional stability and second order in …

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A Positivity Preserving, Energy Stable Finite Difference Scheme For The Flory-Huggins-Cahn-Hilliard-Navier-Stokes System, Wenbin Chen, Jianyu Jing, Cheng Wang, Xiaoming Wang Aug 2022

A Positivity Preserving, Energy Stable Finite Difference Scheme For The Flory-Huggins-Cahn-Hilliard-Navier-Stokes System, Wenbin Chen, Jianyu Jing, Cheng Wang, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we propose and analyze a finite difference numerical scheme for the Cahn-Hilliard-Navier-Stokes system, with logarithmic Flory-Huggins energy potential. in the numerical approximation to the singular chemical potential, the logarithmic term and the surface diffusion term are implicitly updated, while an explicit computation is applied to the concave expansive term. Moreover, the convective term in the phase field evolutionary equation is approximated in a semi-implicit manner. Similarly, the fluid momentum equation is computed by a semi-implicit algorithm: implicit treatment for the kinematic diffusion term, explicit update for the pressure gradient, combined with semi-implicit approximations to the fluid convection …

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Delay Dynamic Equations On Isolated Time Scales And The Relevance Of One-Periodic Coefficients, Martin Bohner, Tom Cuchta, Sabrina Streipert Jul 2022

Delay Dynamic Equations On Isolated Time Scales And The Relevance Of One-Periodic Coefficients, Martin Bohner, Tom Cuchta, Sabrina Streipert

Mathematics and Statistics Faculty Research & Creative Works

We are motivated by the idea that certain properties of delay differential and difference equations with constant coefficients arise as a consequence of their one-periodic nature. We apply the recently introduced definition of periodicity for arbitrary isolated time scales to linear delay dynamic equations and a class of nonlinear delay dynamic equations. Utilizing a derived identity of higher order delta derivatives and delay terms, we rewrite the considered linear and nonlinear delayed dynamic equations with one-periodic coefficients as a linear autonomous dynamic system with constant matrix. As the simplification of a constant matrix is only obtained for one-periodic coefficients, dynamic …

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Derivation And Analysis Of A Discrete Predator–Prey Model, Sabrina H. Streipert, Gail S.K. Wolkowicz, Martin Bohner Jul 2022

Derivation And Analysis Of A Discrete Predator–Prey Model, Sabrina H. Streipert, Gail S.K. Wolkowicz, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

We derive a discrete predator–prey model from first principles, assuming that the prey population grows to carrying capacity in the absence of predators and that the predator population requires prey in order to grow. The proposed derivation method exploits a technique known from economics that describes the relationship between continuous and discrete compounding of bonds. We extend standard phase plane analysis by introducing the next iterate root-curve associated with the nontrivial prey nullcline. Using this curve in combination with the nullclines and direction field, we show that the prey-only equilibrium is globally asymptotic stability if the prey consumption-energy rate of …

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Error Estimate Of A Decoupled Numerical Scheme For The Cahn-Hilliard-Stokes-Darcy System, Wenbin Chen, Shufen Wang, Yichao Zhang, Daozhi Han, Cheng Wang, Xiaoming Wang Jul 2022

Error Estimate Of A Decoupled Numerical Scheme For The Cahn-Hilliard-Stokes-Darcy System, Wenbin Chen, Shufen Wang, Yichao Zhang, Daozhi Han, Cheng Wang, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We analyze a fully discrete finite element numerical scheme for the Cahn-Hilliard-Stokes-Darcy system that models two-phase flows in coupled free flow and porous media. To avoid a well-known difficulty associated with the coupling between the Cahn-Hilliard equation and the fluid motion, we make use of the operator-splitting in the numerical scheme, so that these two solvers are decoupled, which in turn would greatly improve the computational efficiency. The unique solvability and the energy stability have been proved in Chen et al. (2017, Uniquely solvable and energy stable decoupled numerical schemes for the Cahn-Hilliard-Stokes-Darcy system for two-phase flows in karstic geometry. …

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Nonoscillatory Solutions Of Higher-Order Fractional Differential Equations, Martin Bohner, Said R. Grace, Irena Jadlovská, Nurten Kılıç Jun 2022

Nonoscillatory Solutions Of Higher-Order Fractional Differential Equations, Martin Bohner, Said R. Grace, Irena Jadlovská, Nurten Kılıç

Mathematics and Statistics Faculty Research & Creative Works

This paper deals with the asymptotic behavior of the nonoscillatory solutions of a certain forced fractional differential equations with positive and negative terms, involving the Caputo fractional derivative. The results obtained are new and generalize some known results appearing in the literature. Two examples are also provided to illustrate the results.

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