Numerical Methods For Partial Differential Equations

  title={Numerical Methods For Partial Differential Equations},
  author={Marcel Bauer},
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Non linear second order partial differential equations as generalized inverse moment problems
Abstract General forms for non linear elliptic, hyperbolic and parabolic partial differential equations are considered. For all these we present a general procedure that transforms they into aExpand
Linear Partial Differential Equations of First Order as Bi-Dimensional Inverse Moments Problem
We consider linear partial differential equations of first order on a region . We will see that we can write the equation in partial derivatives as an Fredholm integral equation of the first kind andExpand
Application of Cubic Spline Collocation Method for the Numerical Solution of Parabolic Partial Differential Equations
235 Abstract— This work deals with the computational techniques for solving initial boundary value problems in parabolic partial differential equations. The whole idea of the techniques is based onExpand
Parabolic Partial Differential Equations with Border Conditions of Dirichlet as Inverse Moments Problem
We considerer parabolic partial differential equations: under the conditions , on a region . We will see that an approximate solution can be found using the techniques of generalized inverse momentsExpand
Numeric Methods for the Laplace Heat Equation in a Plate
This document presents the concept of the finite difference method for the solution of partial differential equations applied to Laplace's equation. Using its equation to calculate the heatExpand
Numerical Solution of a Two Dimensional Poisson Equation with Dirichlet Boundary Conditions
In this paper we have introduced Numerical techniques to solve a two dimensional Poisson equation together with Dirichlet boundary conditions. Specifically two methods are used for the purpose ofExpand
Operational method of solution of linear non-integer ordinary and partial differential equations
The examples of solution of physical problems, related to such problems as the heat propagation in various models, evolutional processes, Black–Scholes-like equations etc are demonstrated by the operational technique. Expand
Finite Difference Discretization of the Laplace and Poisson Equations. Application to the Anular Ring (donut)
Among the more common numeric methods of solution for partial differential equations (PDE) we have the finite differences method and the finite elements method that approach the real solution throughExpand
Implementation of Numerical Methods for Partial Differential Equation Using Parallel Computing
The performance and use of parallel computing in the field of differential calculus is increased tremendously opening up new avenues for applying these in the field of numerical computation for highExpand
A Study on Applications of Partial Differential Equation and Its Pelation with Fourier
The aim of this paper is to study the partial differential equation and its applications. The research also aims at studying the relation between partial differential equation and Fourier. TheExpand


Numerical solution of partial differential equations by the finite element method
Professor Johnson presents an easily accessible introduction to one of the most important methods used to solve partial differential equations. The bulk of the text focuses on linear problems,Expand
Numerical Approximation of Partial Differential Equations
This is the softcover reprint of the very popular hardcover edition. This book deals with the numerical approximation of partial differential equations. Its scope is to provide a thoroughExpand
Finite Difference Schemes and Partial Differential Equations
Preface to the second edition Preface to the first edition 1. Hyperbolic partial differential equations 2. Analysis of finite difference Schemes 3. Order of accuracy of finite difference schemes 4.Expand
The Mathematical Theory of Finite Element Methods
Contents: Basic Concepts.- Sobolev Spaces.- Variational Formulation of Elliptic Boundary Value Problems.- The Construction of a Finite Element Space.- Polynomial Approximation Theory in SobolevExpand
Adaptive Numerical Solution of PDEs
The theoretical derivation und analyses of algorithms are kept as elementary as possible in this book; the needed sligtly advanced mathematical theory is summarized in the appendix. Expand
Conforming and nonconforming finite element methods for solving the stationary Stokes equations I
— The paper is devoted to a gênerai finite element approximation ofthe solution of the Stokes équations for an incompressible viscous fluid, Both conforming and nonconforming finite element methodsExpand
The Theory of Difference Schemes
Preliminaries basic concepts of the theory of difference schemes homogeneous difference schemes difference schemes for elliptic equations different schemes for time-dependent equations with constantExpand
The finite element method for elliptic problems
  • P. Ciarlet
  • Engineering, Mathematics
  • Classics in applied mathematics
  • 2002
From the Publisher: This book is particularly useful to graduate students, researchers, and engineers using finite element methods. The reader should have knowledge of analysis and functionalExpand
Finite element interpolation of nonsmooth functions satisfying boundary conditions
In this paper, we propose a modified Lagrange type interpolation operator to approximate functions in Sobolev spaces by continuous piecewise polynomials. In order to define interpolators for "rough"Expand
Partial Differential Equations
THE appearance of these volumes marks the happy conclusion of a work undertaken, as the author reminds us in his preface, twenty-one years ago. Doubtless it would have been finished earlier had itExpand