Topic
Order of accuracy
About: Order of accuracy is a research topic. Over the lifetime, 4447 publications have been published within this topic receiving 122522 citations.
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TL;DR: In this paper, a finite-difference method for solving the time-dependent Navier-Stokes equations for an incompressible fluid is introduced, which is equally applicable to problems in two and three space dimensions.
Abstract: A finite-difference method for solving the time-dependent Navier- Stokes equations for an incompressible fluid is introduced. This method uses the primitive variables, i.e. the velocities and the pressure, and is equally applicable to problems in two and three space dimensions. Test problems are solved, and an ap- plication to a three-dimensional convection problem is presented.
4,991 citations
26 Sep 2001
TL;DR: 1. The numerical evaluation of expressions 2. Linear systems of equations 3. Interpolation and numerical differentiation 4. Numerical integration 5. Univariate non linear equations 6. Systems of nonlinear equations.
Abstract: Numerical analysis is an increasingly important link between pure mathematics and its application in science and technology. This textbook provides an introduction to the justification and development of constructive methods that provide sufficiently accurate approximations to the solution of numerical problems, and the analysis of the influence that errors in data, finite-precision calculations, and approximation formulas have on results, problem formulation and the choice of method. It also serves as an introduction to scientific programming in MATLAB, including many simple and difficult, theoretical and computational exercises. A unique feature of this book is the consequent development of interval analysis as a tool for rigorous computation and computer assisted proofs, along with the traditional material.
3,746 citations
TL;DR: An hierarchy of uniformly high-order accurate schemes is presented which generalizes Godunov's scheme and its second- order accurate MUSCL extension to an arbitrary order of accuracy.
2,891 citations
Book•
01 Aug 1994
TL;DR: In this article, the authors provide a thorough illustration of numerical methods, carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation.
Abstract: 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 thorough illustration of numerical methods, carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is one of its main features. Many kinds of problems are addressed. A comprehensive theory of Galerkin method and its variants, as well as that of collocation methods, are developed for the spatial discretization. These theories are then specified to two numerical subspace realizations of remarkable interest: the finite element method and the spectral method.
2,383 citations
TL;DR: In this paper, the equations of hydrodynamics are modified by the inclusion of additional terms which greatly simplify the procedures needed for stepwise numerical solution of the equations in problems involving shocks.
Abstract: The equations of hydrodynamics are modified by the inclusion of additional terms which greatly simplify the procedures needed for stepwise numerical solution of the equations in problems involving shocks. The quantitative influence of these terms can be made as small as one wishes by choice of a sufficiently fine mesh for the numerical integrations. A set of difference equations suitable for the numerical work is given, and the condition that must be satisfied to insure their stabilty is derived.
1,953 citations