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Partial Differential Equations Commons

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Full-Text Articles in Partial Differential Equations

Using A Sand Tank Groundwater Model To Investigate A Groundwater Flow Model, Christopher Evrard, Callie Johnson, Michael A. Karls, Nicole Regnier Jan 2024

Using A Sand Tank Groundwater Model To Investigate A Groundwater Flow Model, Christopher Evrard, Callie Johnson, Michael A. Karls, Nicole Regnier

CODEE Journal

A Sand Tank Groundwater Model is a tabletop physical model constructed of plexiglass and filled with sand that is typically used to illustrate how groundwater water flows through an aquifer, how water wells work, and the effects of contaminants introduced into an aquifer. Mathematically groundwater flow through an aquifer can be modeled with the heat equation. We will show how a Sand Tank Groundwater Model can be used to simulate groundwater flow through an aquifer with a no flow boundary condition.


Analytic Solution Of 1d Diffusion-Convection Equation With Varying Boundary Conditions, Małgorzata B. Glinowiecka-Cox Jun 2022

Analytic Solution Of 1d Diffusion-Convection Equation With Varying Boundary Conditions, Małgorzata B. Glinowiecka-Cox

University Honors Theses

A diffusion-convection equation is a partial differential equation featuring two important physical processes. In this paper, we establish the theory of solving a 1D diffusion-convection equation, subject to homogeneous Dirichlet, Robin, or Neumann boundary conditions and a general initial condition. Firstly, we transform the diffusion-convection equation into a pure diffusion equation. Secondly, using a separation of variables technique, we obtain a general solution formula for each boundary type case, subject to transformed boundary and initial conditions. While eigenvalues in the cases of Dirichlet and Neumann boundary conditions can be constructed easily, the Robin boundary condition necessitates solving a transcendental algebraic …


Analytical Solutions For The Black-Scholes Equation, Jalil Manafian, Mahnaz Paknezhad Dec 2017

Analytical Solutions For The Black-Scholes Equation, Jalil Manafian, Mahnaz Paknezhad

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the Black-Sholes equation (BS) has been applied successfully with the Cauchy-Euler method and the method of separation of variables and new analytical solutions have been found. The linear partial differential equation (PDE) transformed to linear ordinary differential equation (ODE) as well. We acquired three types of solutions including hyperbolic, trigonometric and rational solutions. Descriptions of these methods are given and the obtained results reveal that three methods are tools for exploring partial differential models.


4. Dragging Along, Ruth Dover Jan 2016

4. Dragging Along, Ruth Dover

Differential Equations

More information on air drag.


2. Population, Ruth Dover Jan 2016

2. Population, Ruth Dover

Differential Equations

Introduction to logistic population growth.


3: Drugs And De's, Ruth Dover Jan 2016

3: Drugs And De's, Ruth Dover

Differential Equations

Making a connection between discrete recursion and differential equations.


1. Coffee, Ruth Dover Jan 2016

1. Coffee, Ruth Dover

Differential Equations

Newton’s Law of Cooling.