Partial Differential Equations Research Papers

The aim of this paper is to design the mathematical model of groundwater flow. Groundwater is not static, it flows in an aquifer and its flow can be described using partial differential equation and associated initial-boundary conditions.... more

Since the first volume of this work came out in Germany in 1924, this book, together with its second volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical... more

Bookmark
Download
- by Javier Rodríguez
- •
- 6
  Mathematics, Calculus, Partial Differential Equations, Physics

Since the first volume of this work came out in Germany in 1924, this book has remained a classic in its field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical... more

Bookmark
Download
- by Javier Rodríguez
- •
- 6
  Mathematics, Calculus, Partial Differential Equations, Physics

A method is proposed for deriving dynamical equations for systems with both rigid and flexible components. During the derivation, each flexible component of the system is represented by a ``surrogate element'''' which... more

This paper illustrates the application of a "Sinc-Galerkin" method to the approximate solution of linear and nonlinear second order ordinary differential equations, and to the approximate solution of some linear elliptic and... more

In this paper we continue the development of our Python-based package for the solution of partial differential equations using spatial discretization techniques such as the finite element method (FEM), but we take it to a higher level... more

The statistics of isotropic homogeneous decaying at moderately large Reynolds number are studied in detail using a Fourier-space band-filtering method on flow fields obtained by direct numerical simulation. Two distinct aspects of the... more

A simple non-quasi-static small-signal equivalent circuit model is derived for the ideal MOSFET wave equation under the gradual channel approximation. This equivalent circuit represents each Y-parameter by its DC small-signal value... more

Advection equations appear often in large-scale mathematical models arising in many fields of science and engineering. The Crank-Nicolson scheme can successfully be used in the numerical treatment of such equations. The accuracy of the... more

—The paper deals with simulation of in-situ uranium leaching technological process, collecting data for forecasting and leaching process control. It provides numerical simulation of uranium in-situ leaching (ISL) using Comsol Multiphysics... more

Bookmark
Download
- by Zhanar Omirbekova and +2
  Mukhanov Bahit
  Azamat Usenov
- •
- 8
  Partial Differential Equations, Modeling, Filtration, Multiphysics

In this paper (part II), we analyze the possible mathematical connections between various equations concerning the Bubbles Multiverse Models, the Balls in partial differential equations, several parameters of Ramanujan mathematics and... more

Objectives: In this paper, we present and employ symbolic Maple software algorithm for solving initial value problems (IVPs) of partial differential equations (PDEs). From the literature, the proposed algorithm exhibited a great... more

This paper is concerned with an analog computing based on Cellular Neural Network (CNN) systems to develop an approximate solution of Burgers' equation. The Reaction-diffusion CNN (RD-CNN) model is explained, which is an important class... more

The term Lax Pairs refers to a set of two operators that, if they exist, indicate that a corresponding particular evolution equation is integrable. They represent a pair of differential operators having a characteristic whereby they... more

Bookmark
Download
- by Laure Blanc-feraud and +1
  Josiane Zerubia
- •
- 17
  Information Systems, Partial Differential Equations, Image Processing, Image segmentation

Los siguientes ejercicios o problemas son encontrados en las paginas 47 y 48 del
libro Ecuaciones diferenciales y problemas con valores de frontera, 4 edición.
De Nagle, Saff y Snider.

Bookmark
Download
- by Benjamin Dolgin and +1
  S. Sherrit
- •
- 13
  Partial Differential Equations, Equivalent Circuit, Wave Equation, Capacitance

En el siglo XVIII, el físico-matemático suizo L. Euler comenzó a desarrollar el método del Cálculo Variacional, que llegó a convertirse en uno de los instrumentos más importantes tanto en Matemáticas como en Física y que tendría después... more

En el siglo XVIII, el físico-matemático suizo L. Euler comenzó a desarrollar el método del Cálculo Variacional, que llegó a convertirse en uno de los instrumentos más importantes tanto en Matemáticas como en Física y que tendría después importantes repercusiones en otras áreas como la economía y la conocida optimización dinámica. El propósito de Euler se concentraba en encontrar aquellas curvas con longitudes ya sea máxima o mínima que cumplieran ciertas condiciones iniciales (como pueden ser los valores frontera fijos). De allí que tiempo después Joseph Louis Lagrange aplico varios de los métodos de Euler a ciertos problemas de optimización entre los cuales se encontraba uno muy particular el cual consistía en encontrar una superficie que realizase un mínimo del funcional área y que tuviese valores frontera fijos, que tiempo después sería llamado Problema de Plateau en honor al físico belga Joseph Plateau quien experimento con películas de jabón. Con todo ello, la historia de las superficies minimales tiene su inicio con L. Lagrange, el cual en su memoria \textit{Essai d’une nouvelle méthode pour déterminer les maxima et minima des formules intégrales indéfinies}, desarrollo un interesante algoritmo para el cálculo de variaciones que origino lo que hoy conocemos como la ecuación diferencial de Euler–Lagrange. De esta manera surge la teoría de superficies minimales en $\mathbb{R}^3$. Dicho problema fue planteado tiempo después como encontrar aquellas superficies que tuvieran una curvatura media nula llamadas superficies minimales. Aunque para Lagrange también era importante estudiar aquellas con curvatura media constante. En 1776 Jean Baptiste Marie Meusnier encontró que el plano, el helicoide y la catenoide eran soluciones al problema, además mostro que la ecuación de Euler-Lagrange podía ser modificada a una que se vería relacionada con la expresión de curvatura media. Tiempo después sería un caso particular de la ecuación diferencial de Monge-Ampère. Gaspard Monge y Legendre en 1795 dedujeron las fórmulas para representar las superficies solución. Schwarz encontró la solución del problema de Plateau para un cuadrilátero regular en 1865 y para un cuadrilátero general en 1867 (permitiendo la construcción de sus familias de superficies periódicas) utilizando métodos complejos. Weierstrass y Enneper desarrollaron fórmulas de representación más útiles, enlazando firmemente las superficies minimales al análisis complejo y a las funciones armónicas. La solución completa del problema de Plateau por Jesse Douglas y Tibor Radó fue un hito importante. El descubrimiento en 1982 por Celso Costa de una superficie que refutaba la conjetura de que el plano, la catenoide, y el helicoide son las únicas superficies minimales completas embebidas en $\mathbb{R}^{3}$ de tipo topológico finito. Actualmente la teoría de superficies minimales se ha diversificado a otros ambientes geométricos, adquiriendo importancia en la física matemática (por ejemplo en la conjetura de masa positiva, o en la conjetura de Penrose) y en la geometría de tres variedades (por ejemplo, en la conjetura de Smith, en la conjetura de Poincaré, y en la Conjetura de Geometrización de Thurston)

A partial differential equation (PDE) is an equation containing an unknown function of two or more variables and its partial derivatives with respect to these variables. The order of a PDE is the order of the highest derivative present.... more

A partial differential equation (PDE) is an equation containing an unknown function of two or more variables and its partial derivatives with respect to these variables. The order of a PDE is the order of the highest derivative present. Example. Consider ∂ 2 u ∂x∂y = 2x − y. The is a PDE of order two or a second-order PDE. Here u is the dependent variable while x and y are independnet variables. A solution of a PDE is any function which satisfies the equation identically. A general solution is a solution which contains a number of arbitrary independent functions equal to the order of the equation. A particular solution is one which can be obtained from the general solution by a particular choice of the arbitrary functions. A singular solution is one which can not be obtained from the general solution by a particular choice of the arbitrary functions. A boundary value problem (BVP) involving a PDE seeks a ll solutions of the equation which satisfy conditions known as boundary conditions Theorems relating to the existence and uniqueness of such solutions are called existence and uniqueness theorems. I. LINEAR PDES The general linear PDE of order two in two independent variable has the form Au xx + Bu xy + Cu yy + Du x + Eu y + F u = G (1) where A, B, ..., G may depend on x and y but not on u. A second-order equation with independent variables x and y which does not have the form (1) is called non-linear. If G = 0 identically the equation is called homogeneous while if G = 0 it is called it is called non-homogeneous. Generalizations to higher-order equations are easily made. Because of the nature of the solutions of (1), the equation is often classified as hyperbolic, parabolic or elliptic according to the B 2 − 4AC being greater than, equal to, or less than zero respectively. II. SOME IMPORTANT PDES A. Vibrating String Equation y tt = a 2 y xx This equation is applicable to the small transverse vibrations of a taut, flexible string such as a violin string, initially located at the x-axis and set into motion. The function y(x, t) is the displacement of any point x of the string at time t. The constant is defined as a 2 = τ µ where τ is the constant tension in the string and µ is the constant mass per unit length of the string. It is assumed that no external forces act on the string and that it vibrates only due to its elasticity. The equation can be easily generalized to higher dimensions.

"Networks are mathematically directed (in practical applications also undirected) graphs and a graph is a one-dimensional abstract complex, i.e., a topological space. Network theory focuses on various topological structures and... more

"Networks are mathematically directed (in practical applications also undirected) graphs and a graph is a one-dimensional abstract complex, i.e., a topological space. Network theory focuses on various topological structures and properties, dynamic properties, and functionality-topology relationship, etc. There are some common mathematical foundations, theories and methodology for network analysis, in which graph theory, statistics, and operational research, etc., are the fundamental sciences of network analysis. Various emerging biological networks, at both micro- and macro- levels, will provide numerous sources for the development of general network theory and methodology and also facilitate the development of theory and methodology of biological networks.

Biological network analysis is a fast moving science. Many core scientific issues, for example, ecological structure, co-evolution, co-extinction and biodiversity conservation in ecology, and cancer development and metabolic regulation in health science, etc., are expected to be addressed by network approaches and network analysis. Network analysis is becoming the core methodology to treat complex biological systems. As the fast development of this area, more and more papers on biological networks are published.

At present explosive numbers of quality papers on biological networks are being published each year. The initiation of the journal, Network Biology, will provide a public and unified platform for the publication of these studies. From this integrated and unique journal, researchers, university teachers and students will thoroughly have an in-depth and complete insight on knowledge, methodology and recent advances of biological networks.

In the view of system dynamics, biological networks are always self-organized systems with emergent, autonomous and adaptive properties. Their dynamics can be represented by agent-based modeling, individual-based modeling and some other methodologies like neural network modeling. Therefore, agent-based modeling, individual-based modeling, self-organization of biological systems, and neural network modeling, etc., fall into the aims and scope of the journal, Network Biology.

The NETWORK BIOLOGY (ISSN 2220-8879) is an open access, peer-reviewed online journal that considers scientific articles in all different areas of network biology. It is the transactions of the International Society of Network Biology.It dedicates to the latest advances in network biology. The goal of this journal is to keep a record of the state-of-the-art research and promote the research work in these fast moving areas. The topics to be covered by Network Biology include, but are not limited to:

•Theories, algorithms and programs of network analysis
•Innovations and applications of biological networks
•Dynamics, optimization and control of biological networks
•Ecological networks, food webs and natural equilibrium
•Co-evolution, co-extinction, biodiversity conservation
•Metabolic networks, protein-protein interaction networks, biochemical reaction networks, gene networks, transcriptional regulatory networks, cell cycle networks, phylogenetic networks, network motifs
•Physiological networks
•Network regulation of metabolic processes, human diseases and ecological systems
•Social networks, epidemiological networks
•System complexity, self-organized systems, emergence of biological systems, agent-based modeling, individual-based modeling, neural network modeling, and other network-based modeling, etc.
We are also interested in short communications that clearly address a specific issue or completely present a new ecological network, food web, or metabolic or gene network, etc.

Authors can submit their works to the email box of this journal, networkbiology@iaees.org. All manuscripts submitted to this journal must be previously unpublished and may not be considered for publication elsewhere at any time during review period of this journal. Authors are asked to read Author Guidelines before submitting manuscripts.

In addition to free submissions from authors around the world, special issues are also accepted. The organizer of a special issue can collect submissions (yielded from a research project, a research group, etc.) on a specific research topic, or submissions of a scientific conference for publication of special issue.

Network Biology
ISSN 2220-8879
URL: http://www.iaees.org/publications/journals/nb/online-version.asp
RSS feed: http://www.iaees.org/publications/journals/nb/rss.xml
E-mail: networkbiology@iaees.org
Editor-in-Chief: WenJun Zhang"

The paper deals with the methods of simulation of signal propagation on transmission lines when skin effect is taken into account. Such simulations are useful when solving signal integrity issues in todays high-speed electronic circuits... more

—The paper deals with the methods of simulation of signal propagation on transmission lines when skin effect is taken into account. Such simulations are useful when solving signal integrity issues in todays high-speed electronic circuits... more

This book, authored jointly with A.Tsikh, treats modern analytic aspects of hypergeometric theory in a multidimensional complex space.

The Central Limit Theorem has been described as one of the most remarkable results in all of mathematics and a dominating personality in the world of probability and statistics (Adams, 1974, p. 2). It is one of the oldest results in... more

Differential equations play a relevant role in many disciplines and provide powerful tools for analysis and modeling in applied sciences. The book contains several classical and modern methods for the study of ordinary and partial... more

Bookmark
Download
- by Tom Bertalan
- •
- 4
  Partial Differential Equations, Numerical Analysis, Python, Multigrid

The aim of this paper is to solve numerically the Cauchy problems of nonlinear partial differential equation (PDE) in a modified variational iteration approach. The standard variational iteration method (VIM) is first studied before... more

Partial Differential Equations

Log In