Difference Schemes With Operator Factors
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| Author | : A.A. Samarskii |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 390 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 9401598746 |
Two-and three-level difference schemes for discretisation in time, in conjunction with finite difference or finite element approximations with respect to the space variables, are often used to solve numerically non stationary problems of mathematical physics. In the theoretical analysis of difference schemes our basic attention is paid to the problem of sta bility of a difference solution (or well posedness of a difference scheme) with respect to small perturbations of the initial conditions and the right hand side. The theory of stability of difference schemes develops in various di rections. The most important results on this subject can be found in the book by A.A. Samarskii and A.V. Goolin [Samarskii and Goolin, 1973]. The survey papers of V. Thomee [Thomee, 1969, Thomee, 1990], A.V. Goolin and A.A. Samarskii [Goolin and Samarskii, 1976], E. Tad more [Tadmor, 1987] should also be mentioned here. The stability theory is a basis for the analysis of the convergence of an approximative solu tion to the exact solution, provided that the mesh width tends to zero. In this case the required estimate for the truncation error follows from consideration of the corresponding problem for it and from a priori es timates of stability with respect to the initial data and the right hand side. Putting it briefly, this means the known result that consistency and stability imply convergence.
| Author | : Petr N. Vabishchevich |
| Publisher | : Walter de Gruyter |
| Total Pages | : 370 |
| Release | : 2013-11-27 |
| Genre | : Mathematics |
| ISBN | : 3110321467 |
Applied mathematical modeling is concerned with solving unsteady problems. Splitting schemes are attributed to the transition from a complex problem to a chain of simpler problems. This book shows how to construct additive difference schemes (splitting schemes) to solve approximately unsteady multi-dimensional problems for PDEs. Two classes of schemes are highlighted: methods of splitting with respect to spatial variables (alternating direction methods) and schemes of splitting into physical processes. Also regionally additive schemes (domain decomposition methods) and unconditionally stable additive schemes of multi-component splitting are considered for evolutionary equations of first and second order as well as for systems of equations. The book is written for specialists in computational mathematics and mathematical modeling. All topics are presented in a clear and accessible manner.
| Author | : Sergey Lemeshevsky |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 248 |
| Release | : 2016-09-26 |
| Genre | : Mathematics |
| ISBN | : 311049132X |
Exact Finite-Difference Schemes is a first overview of the topic also describing the state-of-the-art in this field of numerical analysis. Construction of exact difference schemes for various parabolic and elliptic partial differential equations are discussed, including vibrations and transport problems. After this, applications are discussed, such as the discretisation of ODEs and PDEs and numerical methods for stochastic differential equations. Contents: Basic notation Preliminary results Hyperbolic equations Parabolic equations Use of exact difference schemes to construct NSFD discretizations of differential equations Exact and truncated difference schemes for boundary-value problem Exact difference schemes for stochastic differential equations Numerical blow-up time Bibliography
| Author | : Lubin Vulkov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 628 |
| Release | : 1997-02-26 |
| Genre | : Computers |
| ISBN | : 9783540625988 |
This book constitutes the refereed proceedings of the First International Workshop on Numerical Analysis and Its Applications, WNAA'96, held in Rousse, Bulgaria, in June 1996. The 57 revised full papers presented were carefully selected and reviewed for inclusion in the volume; also included are 14 invited presentations. All in all, the book offers a wealth of new results and methods of numerical analysis applicable in computational science, particularly in computational physics and chemistry. The volume reflects that the cooperation of computer scientists, mathematicians and scientists provides new numerical tools for computational scientists and, at the same time, stimulates numerical analysis.
| Author | : Kusum Deep |
| Publisher | : Springer |
| Total Pages | : 416 |
| Release | : 2017-04-12 |
| Genre | : Technology & Engineering |
| ISBN | : 9811033250 |
This two-volume book gathers the proceedings of the Sixth International Conference on Soft Computing for Problem Solving (SocProS 2016), offering a collection of research papers presented during the conference at Thapar University, Patiala, India. Providing a veritable treasure trove for scientists and researchers working in the field of soft computing, it highlights the latest developments in the broad area of “Computational Intelligence” and explores both theoretical and practical aspects using fuzzy logic, artificial neural networks, evolutionary algorithms, swarm intelligence, soft computing, computational intelligence, etc.
| Author | : Ivan Lirkov |
| Publisher | : Springer Nature |
| Total Pages | : 557 |
| Release | : 2022-03-17 |
| Genre | : Computers |
| ISBN | : 3030975495 |
This book constitutes revised selected papers from the 13th International Conference on Large-Scale Scientific Computing, LSSC 23021, which was held in Sozopol, Bulgaria, during June 7-11, 2021. The 60 papers included in this book were carefully reviewed and selected from a total of 73 submissions. The volume also includes two invited talks in full paper length. The papers were organized in topical sections as follows: Fractional diffusion problems: numerical methods, algorithms and applications; large-scale models: numerical methods, parallel computations and applications; application of metaheuristics to large-scale problems; advanced discretizations and solvers for coupled systems of partial differential equations; optimal control of ODEs, PDEs and applications; tensor and matrix factorization for big-data analysis; machine learning and model order reduction for large scale predictive simulations; HPC and big data: algorithms and applications; and contributed papers.
| Author | : Oleg P. Iliev |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 334 |
| Release | : 2013-06-04 |
| Genre | : Mathematics |
| ISBN | : 1461471729 |
One of the current main challenges in the area of scientific computing is the design and implementation of accurate numerical models for complex physical systems which are described by time dependent coupled systems of nonlinear PDEs. This volume integrates the works of experts in computational mathematics and its applications, with a focus on modern algorithms which are at the heart of accurate modeling: adaptive finite element methods, conservative finite difference methods and finite volume methods, and multilevel solution techniques. Fundamental theoretical results are revisited in survey articles and new techniques in numerical analysis are introduced. Applications showcasing the efficiency, reliability and robustness of the algorithms in porous media, structural mechanics and electromagnetism are presented. Researchers and graduate students in numerical analysis and numerical solutions of PDEs and their scientific computing applications will find this book useful.
| Author | : Jose E. Castillo |
| Publisher | : CRC Press |
| Total Pages | : 261 |
| Release | : 2013-01-10 |
| Genre | : Mathematics |
| ISBN | : 1466513438 |
To help solve physical and engineering problems, mimetic or compatible algebraic discretization methods employ discrete constructs to mimic the continuous identities and theorems found in vector calculus. Mimetic Discretization Methods focuses on the recent mimetic discretization method co-developed by the first author. Based on the Castillo-Grone operators, this simple mimetic discretization method is invariably valid for spatial dimensions no greater than three. The book also presents a numerical method for obtaining corresponding discrete operators that mimic the continuum differential and flux-integral operators, enabling the same order of accuracy in the interior as well as the domain boundary. After an overview of various mimetic approaches and applications, the text discusses the use of continuum mathematical models as a way to motivate the natural use of mimetic methods. The authors also offer basic numerical analysis material, making the book suitable for a course on numerical methods for solving PDEs. The authors cover mimetic differential operators in one, two, and three dimensions and provide a thorough introduction to object-oriented programming and C++. In addition, they describe how their mimetic methods toolkit (MTK)—available online—can be used for the computational implementation of mimetic discretization methods. The text concludes with the application of mimetic methods to structured nonuniform meshes as well as several case studies. Compiling the authors’ many concepts and results developed over the years, this book shows how to obtain a robust numerical solution of PDEs using the mimetic discretization approach. It also helps readers compare alternative methods in the literature.
| Author | : Bernd Aulbach |
| Publisher | : CRC Press |
| Total Pages | : 590 |
| Release | : 2004-06-07 |
| Genre | : Mathematics |
| ISBN | : 9780203575437 |
This volume comprises selected papers presented at the Sixth International Conference on Difference Equations which was held at Augsburg, Germany. It covers all themes in the fields of discrete dynamical systems and ordinary and partial difference equations, classical and contemporary, theoretical and applied. It provides a useful reference text for graduates and researchers working in this area of mathematics.
| Author | : Ivan Dimov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 524 |
| Release | : 2011-01-14 |
| Genre | : Computers |
| ISBN | : 3642184650 |
This book constitutes the thoroughly refereed post-conference proceedings of the 7th International Conference on Numerical Methods and Applications, NMA 2010, held in Borovets, Bulgaria, in August 2010. The 60 revised full papers presented together with 3 invited papers were carefully reviewed and selected from numerous submissions for inclusion in this book. The papers are organized in topical sections on Monte Carlo and quasi-Monte Carlo methods, environmental modeling, grid computing and applications, metaheuristics for optimization problems, and modeling and simulation of electrochemical processes.
