Compact Finite Difference Schemes for Mixed Initial-boundary Value Problems PDF Download
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Author: Richard B. Philips
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 56
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Book Description
"This paper discusses a class of compact second order accurate finite difference equations for mixed initial-boundary value problems for hyperbolic and convective-diffusion equations. Convergence is proved by means of an energy argument and both types of equations are solved by similar algorithms. For hyperbolic equations an extension of the Lax-Wendroff method is described which incorporates dissipative boundary conditions. Upwind-downwind differencing techniques arise as the formal hyperbolic limit of the convective-diffusion equation. Finally, a finite difference 'chain-rule' transforms the schemes from rectangular to quadrilateral subdomains" -- abstract.
Author: Richard B. Philips
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 56
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Book Description
"This paper discusses a class of compact second order accurate finite difference equations for mixed initial-boundary value problems for hyperbolic and convective-diffusion equations. Convergence is proved by means of an energy argument and both types of equations are solved by similar algorithms. For hyperbolic equations an extension of the Lax-Wendroff method is described which incorporates dissipative boundary conditions. Upwind-downwind differencing techniques arise as the formal hyperbolic limit of the convective-diffusion equation. Finally, a finite difference 'chain-rule' transforms the schemes from rectangular to quadrilateral subdomains" -- abstract.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 30
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Book Description
Author: Ivan Gavrilyuk
Publisher: Springer Science & Business Media
ISBN: 3034801076
Category : Mathematics
Languages : en
Pages : 247
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Book Description
The book provides a comprehensive introduction to compact finite difference methods for solving boundary value ODEs with high accuracy. The corresponding theory is based on exact difference schemes (EDS) from which the implementable truncated difference schemes (TDS) are derived. The TDS are now competitive in terms of efficiency and accuracy with the well-studied numerical algorithms for the solution of initial value ODEs. Moreover, various a posteriori error estimators are presented which can be used in adaptive algorithms as important building blocks. The new class of EDS and TDS treated in this book can be considered as further developments of the results presented in the highly respected books of the Russian mathematician A. A. Samarskii. It is shown that the new Samarskii-like techniques open the horizon for the numerical treatment of more complicated problems. The book contains exercises and the corresponding solutions enabling the use as a course text or for self-study. Researchers and students from numerical methods, engineering and other sciences will find this book provides an accessible and self-contained introduction to numerical methods for solving boundary value ODEs.
Author: Jonathan Tyler
Publisher:
ISBN:
Category : Burgers equation
Languages : en
Pages : 102
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Book Description
The derivation of centered compact schemes at interior and boundary grid points is performed and an analysis of stability and computational efficiency is given. Compact schemes are high order implicit methods for numerical solutions of initial and/or boundary value problems modeled by differential equations. These schemes generally require smaller stencils than the traditional explicit finite difference counterparts. To avoid numerical instabilities at and near boundaries and in regions of mesh non-uniformity, a numerical filtering technique is employed. Experiments for non-stationary linear problems (convection, heat conduction) and also for nonlinear problems (Burgers' and KdV equations) were performed. The compact solvers were combined with Euler and fourth-order Runge-Kutta time differencing. In most cases, the order of convergence of the numerical solution to the exact solution was the same as the formal order of accuracy of the compact schemes employed.
Author: A.K. Aziz
Publisher: Academic Press
ISBN: 1483267997
Category : Mathematics
Languages : en
Pages : 380
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Book Description
Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations covers the proceedings of the 1974 Symposium by the same title, held at the University of Maryland, Baltimore Country Campus. This symposium aims to bring together a number of numerical analysis involved in research in both theoretical and practical aspects of this field. This text is organized into three parts encompassing 15 chapters. Part I reviews the initial and boundary value problems. Part II explores a large number of important results of both theoretical and practical nature of the field, including discussions of the smooth and local interpolant with small K-th derivative, the occurrence and solution of boundary value reaction systems, the posteriori error estimates, and boundary problem solvers for first order systems based on deferred corrections. Part III highlights the practical applications of the boundary value problems, specifically a high-order finite-difference method for the solution of two-point boundary-value problems on a uniform mesh. This book will prove useful to mathematicians, engineers, and physicists.
Author: Yuval Harness
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 360
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Book Description
![Finite Difference Methods for the First Boundary Value Problem of [delta]u(x, Y) PDF](https://books.google.com/books/content/images/frontcover/D5KJdZawfiIC?fife=w80-h100)
Author: Werner Uhlmann
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 178
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Book Description
Author: Institute for Computer Applications in Science and Engineering
Publisher:
ISBN:
Category :
Languages : en
Pages : 66
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Book Description
Author: Boško S. Jovanović
Publisher: Matematicki Institut
ISBN:
Category : Boundary value problems
Languages : en
Pages : 102
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Book Description
Author: Herbert Bishop Keller
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 416
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Book Description
A brief, elementary yet rigorous account of practical numerical methods for solving very general two-point boundary-value problems. Advanced undergraduate level. Over 100 problems.
