scholarly journals Development of GIS-based Python scripts to calculate a water surface profile on a landscape for wetlands decision-making

2020 ◽  
Vol 22 (3) ◽  
pp. 628-640
Author(s):  
Zhentao Wang ◽  
Kathleen M. Trauth
Keyword(s):  
Water Surface ◽  
Research Effort ◽  
Land Use Changes ◽  
Surface Profile ◽  
Euler’S Method ◽  
Landscape Characteristics ◽  
Landscape Processes ◽  
Mitigation Wetland ◽  
Elevation Model ◽  
Channel Hydraulics

Abstract Wetlands provide many benefits for humans and the natural environment, but land-use changes have reduced their number and areal extent. Interest has grown in examining the landscape to determine those locations where, with minimal effort, it might be possible to develop a mitigation wetland – a location with sufficient water over a sufficient period of time to develop and maintain wetland functioning. This paper proposes a methodology to support the examination of the landscape for mitigation purposes through the application of open channel hydraulics principles to flow over a landscape. The methodology is part of a larger research effort ultimately combining hydrology and hydraulics, along with the landscape processes of infiltration and evapotranspiration, to perform a water balance assessment. Specifically, the methodology is implemented through readily available geographic information system tools along with Python scripts written for this study. The Python scripts automatically extract landscape characteristics from a digital elevation model and calculate hydraulic parameters that are used to determine water surface profiles using the Modified Euler's method. Multiple tests show that the script accurately produces profiles of flow between depressions over a landscape. Such determinations are the first step in understanding where water might exist on the surface to support mitigation wetland functions.

scholarly journals Stability analysis of linear conformable fractional differential equations system with time delays

2019 ◽  
Vol 38 (6) ◽  
pp. 159-171 ◽  
Author(s):  
Vahid Mohammadnezhad ◽  
Mostafa Eslami ◽  
Hadi Rezazadeh
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Differential Equations ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Euler’S Method ◽  
Fractional Differential ◽  
Theoretical Results

In this paper, we first study stability analysis of linear conformable fractional differential equations system with time delays. Some sufficient conditions on the asymptotic stability for these systems are proposed by using properties of the fractional Laplace transform and fractional version of final value theorem. Then, we employ conformable Euler’s method to solve conformable fractional differential equations system with time delays to illustrate the effectiveness of our theoretical results

scholarly journals Mean Square Convergent Non-Standard Numerical Schemes for Linear Random Differential Equations with Delay

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1417 ◽  
Author(s):  
Julia Calatayud ◽  
Juan Carlos Cortés ◽  
Marc Jornet ◽  
Francisco Rodríguez
Keyword(s):  
Stochastic Process ◽  
Differential Equations ◽  
Random Variables ◽  
Mean Square ◽  
Discrete Delay ◽  
Numerical Schemes ◽  
Recent Contribution ◽  
Order Of Accuracy ◽  
Euler’S Method ◽  
Random Differential Equations

In this paper, we are concerned with the construction of numerical schemes for linear random differential equations with discrete delay. For the linear deterministic differential equation with discrete delay, a recent contribution proposed a family of non-standard finite difference (NSFD) methods from an exact numerical scheme on the whole domain. The family of NSFD schemes had increasing order of accuracy, was dynamically consistent, and possessed simple computational properties compared to the exact scheme. In the random setting, when the two equation coefficients are bounded random variables and the initial condition is a regular stochastic process, we prove that the randomized NSFD schemes converge in the mean square (m.s.) sense. M.s. convergence allows for approximating the expectation and the variance of the solution stochastic process. In practice, the NSFD scheme is applied with symbolic inputs, and afterward the statistics are explicitly computed by using the linearity of the expectation. This procedure permits retaining the increasing order of accuracy of the deterministic counterpart. Some numerical examples illustrate the approach. The theoretical m.s. convergence rate is supported numerically, even when the two equation coefficients are unbounded random variables. M.s. dynamic consistency is assessed numerically. A comparison with Euler’s method is performed. Finally, an example dealing with the time evolution of a photosynthetic bacterial population is presented.

scholarly journals Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients

2010 ◽  
Vol 467 (2130) ◽  
pp. 1563-1576 ◽  
Author(s):  
Martin Hutzenthaler ◽  
Arnulf Jentzen ◽  
Peter E. Kloeden
Keyword(s):  
Exact Solution ◽  
Finite Time ◽  
Weak Sense ◽  
Mean Square ◽  
Euler’S Method ◽  
Lipschitz Continuous ◽  
The Difference ◽  
And Diffusion ◽  
Weak Divergence ◽  
Time Point

The stochastic Euler scheme is known to converge to the exact solution of a stochastic differential equation (SDE) with globally Lipschitz continuous drift and diffusion coefficients. Recent results extend this convergence to coefficients that grow, at most, linearly. For superlinearly growing coefficients, finite-time convergence in the strong mean-square sense remains. In this article, we answer this question to the negative and prove, for a large class of SDEs with non-globally Lipschitz continuous coefficients, that Euler’s approximation converges neither in the strong mean-square sense nor in the numerically weak sense to the exact solution at a finite time point. Even worse, the difference of the exact solution and of the numerical approximation at a finite time point diverges to infinity in the strong mean-square sense and in the numerically weak sense.

The Effect of Initial Void Configuration on the Morphological Evolution Under the Action of Normalized Electron Wind Forces

2001 ◽  
Vol 714 ◽  
Author(s):  
Ersin Emre Oren ◽  
Tarik Omer Ogurtani
Keyword(s):  
Morphological Evolution ◽  
Strong Dependence ◽  
Thermodynamic Formalism ◽  
Time Step ◽  
Euler’S Method ◽  
Morphological Variations ◽  
Comprehensive Picture ◽  
Void Shape ◽  
Evolution Dynamics ◽  
Electron Wind

ABSTRACTIn these studies a comprehensive picture of void shape evolution dynamics and its strong dependence on the initial configuration has been thoroughly investigated by utilizing hypocycloid algebra to generate four different shapes of main interest. Our mathematical model on the isotropic diffusion and mass accumulation on void surfaces, under the action of applied electrostatic potential and capillary effects, follows a novel irreversible but discrete thermodynamic formalism of interphases and surfaces.As a result during the intragranual motion, in addition to the crescent-like slit formation, very rich and also unusual void morphological variations such as fragmentations into the daughter voids or inner island generation have been observed under the severe (normalized) electron wind intensities or very long exposure times. In these numerical experiments, the Euler's method of finite differences with an automatic time step self-adjustment has been utilized in combination with a rather powerful and fast indirect boundary element method (IBEM) for the solution of the Laplace equation.

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