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Search results for: 2D RICHARDS EQUATION
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Numerical Solution of the Two-Dimensional Richards Equation Using Alternate Splitting Methods for Dimensional Decomposition
PublicationResearch on seepage flow in the vadose zone has largely been driven by engineering and environmental problems affecting many fields of geotechnics, hydrology, and agricultural science. Mathematical modeling of the subsurface flow under unsaturated conditions is an essential part of water resource management and planning. In order to determine such subsurface flow, the two-dimensional (2D) Richards equation can be used. However,...
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Computationally Effcient Solution of a 2D Diffusive Wave Equation Used for Flood Inundation Problems
PublicationThis paper presents a study dealing with increasing the computational efficiency in modeling floodplain inundation using a two-dimensional diffusive wave equation. To this end, the domain decomposition technique was used. The resulting one-dimensional diffusion equations were approximated in space with the modified finite element scheme, whereas time integration was carried out using the implicit two-level scheme. The proposed...
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Analysis of Floodplain Inundation Using 2D Nonlinear Diffusive Wave Equation Solved with Splitting Technique
PublicationIn the paper a solution of two-dimensional (2D) nonlinear diffusive wave equation in a partially dry and wet domain is considered. The splitting technique which allows to reduce 2D problem into the sequence of one-dimensional (1D) problems is applied. The obtained 1D equations with regard to x and y are spatially discretized using the modified finite element method with the linear shape functions. The applied modification referring...
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Impact of diffusion coefficient averaging on solution accuracy of the 2D nonlinear diffusive wave equation for floodplain inundation
PublicationIn the study, the averaging technique of diffusion coefficients in the two-dimensional nonlinear diffusive wave equation applied to the floodplain inundation is presented. As a method of solution, the splitting technique and the modified finite element method with linear shape functions are used. On the stage of spatial integration, it is often assumed that diffusion coefficient is constant over element and equal to its average...
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Experimental and Numerical Analysis of Air Trapping in a Porous Medium with Coarse Textured Inclusions
PublicationThe paper presents a 2D upward infiltration experiment performed on a model porous medium consisting of fine sand background with two inclusions made of coarser sands. The purpose of the experiment was to investigate the effects of structural air trapping, which occurs during infiltration as a result of heterogeneous material structure. The experiment shows that a significant amount of air becomes trapped in each of the inclusions. Numerical...
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A Quasi-2D MOSFET Model — 2D-to-Quasi-2D Transformation
PublicationA quasi-two-dimensional (quasi-2D) representation of the MOSFET channel is proposed in this work. The representation lays the foundations for a quasi 2D MOSFET model. The quasi 2D model is a result of a 2D into quasi 2D transformation. The basis for the transformation are an analysis of a current density vector field and such phenomena as Gradual Channel Detachment Effect (GCDE), Channel Thickness Modulation Effect (CTME), and...
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Influence of heterogeneous air entry pressure on large scale unsaturated flow in porous media
PublicationThe paper presents numerical simulations of water infiltration in unsaturated porous media containing coarse-textured inclusions embed- ded in fine-textured background material. The calculations are performed using the two-phase model for water and air flow and a simplified model known as the Richards equation. It is shown that the Richards equation cannot correctly describe flow in the presence of heterogeneities. How- ever, its...
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Examples of numerical simulations of two-dimensional unsaturated flow with VS2DI code using different interblock conductivity averaging schemes
PublicationFlow in unsaturated porous media is commonly described by the Richards equation. This equation is strongly nonlinear due to interrelationships between water pressure head (negative in unsaturated conditions), water content and hydraulic conductivity. The accuracy of numerical solution of the Richards equation often depends on the method used to estimate average hydraulic conductivity between neighboring nodes or cells of the numerical...
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ADAPTIVE METHOD FOR THE SOLUTION OF 1D AND 2D ADVECTION-DIFFUSION EQUATIONS USED IN ENVIRONMENTAL ENGINEERING
PublicationThe paper concerns the numerical solution of one-dimensional (1D) and two-dimensional (2D) advection-diffusion equations. For the numerical solution of the 1D advection-diffusion equation a method, originally proposed for solution of the 1D pure advection equation, has been developed. A modified equation analysis carried out for the proposed method allowed increasing of the resulting solution accuracy and consequently, to reduce...
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A quasi-2D small-signal MOSFET model - main results
PublicationDynamic properties of the MOS transistor under small-signal excitation are determined by kinetic parameters of the carriers injected into the channel, i.e., the low-field mobility, velocity saturation, mobility at the quiescent-point (Q-point), longitudinal electric field in the channel, by dynamic properties of the channel, as well as by an electrical coupling between the perturbed carrier concentration in the channel and the...
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TIME- AND FREQUENCY-DOMAIN QUASI-2D SMALL-SIGNAL MOSFET MODELS
PublicationA novel approach to small-signal MOSFET modeling is presented in this book. As a result, time- and frequency-domain physics-based quasi-2D NQS four-terminal small-signal MOSFET models are proposed. The time-domain model provides the background to a novel DIBL-included quasi‑2D NQS four-terminal frequency-domain small-signal MOSFET model. Parameters and electrical quantities of the frequency-domain model are described by explicit...
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Numerical Simulations of Seepage in Dikes Using unsaturated and Two-Phase Flow Models
PublicationModeling of water flow in variably saturated porous media, including flood dikes, is often based on the Richards equation, which neglects the flow of pore air, assuming that it remains at constant atmospheric pressure. However, there is also evidence that the air flow can be important, especially when the connectivity between the pore air and atmospheric air is lost. In such cases a full two-phase air-water flow model should be...
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Simulations of air and water flow in a model dike during overflow experiments
PublicationFlow in flood dikes, earth dams, and embankments occurs in variably saturated conditions, with pores of the earth material filled partly with water and partly with air. In routine engineering analysis, the influence of pore air is neglected and the air pressure is assumed equal to atmospheric. In some circumstances, for example, during overtopping of the dike by water, the effect of pore air on water flow and stability of the structure...
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Air trapping problem during infiltration on the large areas
PublicationThe process of flow modeling in unsaturated porous medium is often found in many fields of sciences: geology, fluid mechanics, thermodynamics, microbiology or chemistry. Problem is relatively complicated due to complexity of the system which contains three phases: water, air and soil skeleton. The flow of water in such a medium can be described using two-phase (2PH) flow formulation, which accounts the inflow of air and water phases,...
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Simulation of unsteady flow over floodplain using the diffusive wave equation and the modified finite element method
PublicationWe consider solution of 2D nonlinear diffusive wave equation in a domain temporarily covered by a layer of water. A modified finite element method with triangular elements and linear shape functions is used for spatial discretization. The proposed modification refers to the procedure of spatial integration and leads to a more general algorithm involving a weighting parameter. The standard finite element method and the finite difference...
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Investigations On Water Circulation in Animal Sea-Water Basins – On the Example of Seals′ Breeding Pools
PublicationThis paper presents general comments concerning investigations on water circulation in animal breeding pools containing sea water. As an example are given results of computer simulation of water circulation in seals’ breeding pools situated in Marine Station at Hel, belonging to Oceanographic Institute, Gdansk University. A mathematical model of three main pools was prepared with taking into account their inflow and outflow water...
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Flood Modelling and Risk Analysis of Cinan Feizuo Flood Protection Area, Huaihe River Basin
PublicationThis study evaluated multiple aspects of flood risks and effects on the Cinan Feizuo flood protection area in the Huaihe River basin. Flooding remains a leading problem for infrastructure, especially in urban, residential areas of the region. Effective flood modeling for urbanized floodplains is challenging, but MIKE (ID-2D) is paramount for analyzing and quantifying the risk in the vulnerable region. The Saint-Venant equation...
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Influence of the air phase on water flow in dikes
PublicationNumerical models are often used to describe flow and deformation processes occurring in dikes during flood events. Modeling of such phenomena is a challenging task, due to the complexity of the system, consisting of three material phases: soil skeleton, pore water and pore air. Additional difficulties are transient loading caused by variable in time water levels, heterogeneity of the soil or air...
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2D Mathematical Model of the Commutator Sliding Contact of an Electrical Machine
PublicationW artykule przedstawiono model matematyczny 2D komutatorowego zestyku ślizgowego z wieloma stopniami swobody. W modelu uwzględniono zmienne wymuszenia działające na szczotkę. Wymuszenia te są wynikiem falistości wirującego komutatora. Szczotka została zamodelowana jako system wielu mas, elementów sprężystych i tłumików rozłożonych w kierunku stycznym i promieniowym. Zamodelowano wszystkie oddziaływania lepkosprężyste pomiędzy komutatorem...
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Simulations of freshwater lens recharge and salt/freshwater interfaces using the HYDRUS and SWI2 packages for MODFLOW
PublicationThe paper presents an evaluation of the combined use of the HYDRUS and SWI2 packages for MODFLOW as a potential tool for modeling recharge in coastal aquife rs subject to saltwater intrusion. The HYDRUS package for MODFLOW solves numerically the one-dimensional form of the Richards equation describing water flow in variably- saturated media. The code computes groundwater recharge to or...
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Mechanical exfoliation and layer number identification of single crystal monoclinic CrCl3
PublicationAfter the recent finding that CrI3, displays ferromagnetic order down to its monolayer, extensive studies have followed to pursue new two-dimensional (2D) magnetic materials. In this article, we report on the growth of single crystal CrCl3 in the layered monoclinic phase. The system after mechanical exfoliation exhibits stability in ambient air (the degradation occurs on a time scale at least four orders of magnitude longer than...
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Water retention curves of sandy soils obtained from direct measurements, particle size distribution, and infiltration experiments
PublicationAccurate information about soil water retention curves (SWRCs) of sands is essential for evaluating groundwater recharge and vulnerability to contamination in many shallow sandy aquifers which are widespread on post glacial areas in Northern Europe and North America. Pedotransfer functions (PTFs) allow to estimate SWRC from basic physical characteristics of soils, such as textural composition. However, in the case of clean sands...
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Equivariant Morse equation
PublicationThe paper is concerned with the Morse equation for flows in a representation of a compact Lie group. As a consequence of this equation we give a relationship between the equivariant Conley index of an isolated invariant set of the flow given by x˙ = − ∇f(x) and the gradient equivariant degree of ∇f. Some multiplicity results are also presented.
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Dimensionally Consistent Nonlinear Muskingum Equation
PublicationAlthough the Muskingum equation was proposed nearly 75 years ago, it is still a subject of active research. Despite of its simple form, the real properties of this equation have not been comprehensively explained. This paper proposes a new interpretation of the linear McCarthy’s relation. This relation can be interpreted only together with the storage equation, whereas the Muskingum equation can be derived directly from the system...
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Comparison of 2D and 3D culture models in the studies of the biological response induced by unsymmetrical bisacridines in cancer cells
PublicationMulticellular tumor spheroids are a good tool for testing new anticancer drugs, including those that may target cancer stem cells (CSCs), responsible for cancer progression, metastasis, and recurrence. Therefore, following the initial evaluation of the impact of antitumor unsymmetrical bisacridines (UAs) on lung and colon cancer cells using traditional monolayer cultures, I extended my investigations and applied the spherical model....
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2D inverse method of turbomachinery stage design
Publication1. How 2D model for turbomachinery stages has developed historically. 2. Recent understanding of physical background of 2D model. 3. Curvilinear system of non-orthogonal coordinates in the application to 2D model. 4. Set of basic equations. 5. Closing conditions for the inverse problem. 6. Examples of solutions a)
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Newton’s Method for the McKendrick-von Foerster Equation
PublicationIn the paper we study an age-structured model which describes the dynamics of one population with growth, reproduction and mortality rates. We apply Newton’smethod to the McKendrick-von Foerster equation in the semigroup setting. We prove its first- and second-order convergence.
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Thermal ablation modeling via bioheat equation
PublicationWe consider Pennes’ bioheat equation and discuss an implicit numerical scheme which has better stability properties than other approaches. Our discussion concerns Carthesian geometry problems, however it carries over to spherical geometry models and more complicated shapes.
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Balance error generated by numerical diffusion in the solution of Muskingum equation
PublicationIn the paper the conservative properties of the lumped hydrological models with variable parameters are discussed. It is shown that in the case of the non-linear Muskingum equation the mass balance is not satisfied. The study indicates that the mass balance errors are caused by the improper form of equation and by the numerical diffusion which is generated in the solution. It has been shown that the classical way of derivation...
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Identification of Parameters Influencing the Accuracy of the Solution of the Nonlinear Muskingum Equation
PublicationTwo nonlinear versions of the Muskingum equation are considered. The difference between both equations relates to the exponent parameter. In the first version, commonly used in hydrology, this parameter is considered as free, while in the second version, it takes a value resulting from the kinematic wave theory. Consequently, the first version of the equation is dimensionally inconsistent, whereas the proposed second one is consistent. It...
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Numerical Characterization of Thresholds for the Focusing 1d Nonlinear Schrödinger Equation
PublicationThe focusing nonlinear Schrödinger equation arises in various physical phenomena and it is therefore of interest to determine mathematical conditions on the initial data that guarantee whether the corresponding solution will blow up in finite time or exist globally in time. We focus on solutions to the mass‐supercritical nonlinear Schrödinger equation (1) in 1D case. In particular, we investigate numerical thresholds between blow...
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Computational issues of solving the 1D steady gradually varied flow equation
PublicationIn this paper a problem of multiple solutions of steady gradually varied flow equation in the form of the ordinary differential energy equation is discussed from the viewpoint of its numerical solution. Using the Lipschitz theorem dealing with the uniqueness of solution of an initial value problem for the ordinary differential equation it was shown that the steady gradually varied flow equation can have more than one solution....
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Reduced order model of 2d system
PublicationA new method of modelling is developed for static and dynamic analysis of two-dimensional elastic bodies. In the analysis, an elastic body is divided into strips. For each one-dimensional strip the reduced modal model is build up. The modal model contains appropriate number of inputs and outputs to connect lumped interaction that occur between strips. Proposed method of modelling enables to obtain more accurate and more simple...
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Straightened characteristics of McKendrick-von Foerster equation
PublicationWe study the McKendrick-von Foerster equation with renewal (that is the age-structured model, with total population dependent coefficient and nonlinearity). By using a change of variables, the model is then transformed to a standard age-structured model in which the total population dependent coefficient of the transport term reduces to a constant 1. We use this transformation to get existence, uniqueness of solutions of the problem...
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2D MXene nanocomposites: electrochemical and biomedical applications
PublicationIn recent years, key questions about the interaction of 2D MXene nanomaterials in electrochemical and biomedical applications have been raised. Most research has focused on clarifying the exclusive properties of the materials; however, only limited reports have described the biomedical applications of 2D nanomaterials. 2D MXenes are monolayer atomic nanosheets resulting from MAX phase ceramics. The hydrophilic properties, metallic...
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Synthesis, characterization, and application of 2D/2D TiO2-GO-ZnFe2O4 obtained by the fluorine-free lyophilization method for solar light-driven photocatalytic degradation of ibuprofen
PublicationIn this study, we report the potential of 2D/2D TiO2- GO-ZnFe2O4 photocatalyst obtained using the fluorine-free lyophilization technique for the degradation of ibuprofen belonging to the group of active pharmaceutical ingredients (API). The improved ibuprofen degradation under simulated solar light was achieved in the presence of a composite of 2D TiO2 combined with GO and embedded ZnFe2O4, which additionally provides superparamagnetic...
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Flow models 1D, 2D, 3D for diagonal pump
PublicationTrzy typowe modele stosowane w maszynach wirnikowych 1D, 2D, 3D zostały przedstawione w zastosowaniu do przepływu w pompie diagonalnej. W ramach modelu 1D przedstawiono prezentację procesu na wykresie energia -straty. W ramach modelu 2D pokazano wynik rozwiązania zadania odwrotnego prowadzącego do kształtu łopatek wirnika pompy. W ramach modelu 3D wykonano obliczenia programem FLUENT pokazując charakterystyczne cechy dwóch różnie...
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KOLMOGOROV EQUATION SOLUTION: MULTIPLE SCATTERING EXPANSION AND PHOTON STATISTICS EVOLUTION MODELING
PublicationWe consider a formulation of the Cauchy problem for the Kolmogorov equation which corresponds to a localized source of particles to be scattered by a medium with a given scattering amplitude density. The multiple scattering amplitudes are introduced and the corresponding series solution of the equation is constructed. We investigate the integral representation for the first series terms, its estimations and values of the photon...
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Composite 2D Material-Based Pervaporation Membranes for Liquid Separation: A Review
PublicationToday, chemistry and nanotechnology cover molecular separations in liquid and gas states by aiding in the design of new nano-sized materials. In this regard, the synthesis and application of two-dimensional (2D) nanomaterials are current fields of research in which structurally defined 2D materials are being used in membrane separation either in self-standing membranes or composites with polymer phases. For instance, pervaporation...
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Thermal ablation modeling via the bioheat equation and its numerical treatment
PublicationThe phenomenon of thermal ablation is described by Pennes’ bioheat equation. This model is based on Newton’s law of cooling. Many approximate methods have been considered because of the importance of this issue. We propose an implicit numerical scheme which has better stability properties than other approaches.
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A quasi-2D small-signal MOSFET model - main results
PublicationMain results stemming from a new quasi 2D non-quasi-static small-signal four-terminal model of the MOSFET are presented in this work. The model is experimentally verified up to 30 GHz.
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Methods of solving the Atkins equation determine shear angle with taking into consideration a modern fracture mechanics
PublicationIn the paper are presented methods of solving nonlinear Atkins equation . The Atkins equation describe shear angle with taking into account properties of material cutting. To solve Atkins equation has been used iterative methods: Newton method and simplified method of simple iteration. Method of simple iteration is presented in the form of Java application.
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Estimation of a Stochastic Burgers' Equation Using an Ensemble Kalman Filter
PublicationIn this work, we consider a difficult problem of state estimation of nonlinear stochastic partial differential equations (SPDE) based on uncertain measurements. The presented solution uses the method of lines (MoL), which allows us to discretize a stochastic partial differential equation in a spatial dimension and represent it as a system of coupled continuous-time ordinary stochastic differential equations (SDE). For such a system...
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Influence of mesh density on 2D viscous flutter in a turbomachinery cascade
PublicationIn this study numerical simulations of 2D viscous flutter were performed and compared with available experimental results for various mesh densities and flow parameters. Calculations were carried out for the bending oscillations of an Eleventh Standard Configuration cascade. ANSYS CFX code was used for the SST, SA and k-ω turbulence model calculations.
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Considerations about the applicability of the Reynolds equation for analyzing high-speed near field levitation phenomena
Publicationequation for analyzing near field levitation (NFL) phenomena. Two separate approaches were developed, experimentally verified, and applied to meet the research objective. One was based on the Reynolds equation and the other was based on general conservation equations for fluid flow solved using computational fluid dynamic (CFD). Comparing the calculation results revealed that, for certain operating conditions, differences in the...
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Modele 1D i 2D przepływu w pompie diagonalnej
PublicationW pracy przedstawiono nowe podejście do rozwiązania zadania konstrukcyjnego pompy w ramach modelu osiowo-symetrycznego typu 2D. Przykład obliczeniowy cytowany w artykule przedstawia wirnik pompy diagonalnej poddanej obliczeniom 3D.Przedstawiono także nowy sposób prezentacji procesu tłoczenia w pompie diagonalnej w ramach modelu 1D w postaci wykresu energia - straty energii.
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Impact of the Finite Element Mesh Structure on the Solution Accuracy of a Two-Dimensional Kinematic Wave Equation
PublicationThe paper presents the influence of the finite element mesh structure on the accuracy of the numerical solution of a two-dimensional linear kinematic wave equation. This equation was solved using a two-level scheme for time integration and a modified finite element method with triangular elements for space discretization. The accuracy analysis of the applied scheme was performed using a modified equation method for three different...
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Studies of Nonlinear Sound Dynamics in Fluids Based on the Caloric Equation of State
PublicationThe sound speed and parameters of nonlinearity B/A, C/A in a fluid are expressed in terms of coefficients in the Taylor series expansion of an excess internal energy, in powers of excess pressure and density. That allows to conclude about features of the sound propagation in fluids, the internal energy of which is known as a function of pressure and density. The sound speed and parameters of nonlinearity in the mixture consisting...
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On the convergence of a nonlinear finite-difference discretization of the generalized Burgers–Fisher equation
PublicationIn this note, we establish analytically the convergence of a nonlinear finite-difference discretization of the generalized Burgers-Fisher equation. The existence and uniqueness of positive, bounded and monotone solutions for this scheme was recently established in [J. Diff. Eq. Appl. 19, 1907{1920 (2014)]. In the present work, we prove additionally that the method is convergent of order one in time, and of order two in space. Some...
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Equation of state for Eu-doped SrSi2O2N2
Publication