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Difference Schemes with Operator Factors

  • A. A. Samarskii
  • P. P. Matus
  • P. N. Vabishchevich

Part of the Mathematics and Its Applications book series (MAIA, volume 546)

Table of contents

  1. Front Matter
    Pages i-x
  2. A. A. Samarskii, P. P. Matus, P. N. Vabishchevich
    Pages 1-8
  3. A. A. Samarskii, P. P. Matus, P. N. Vabishchevich
    Pages 9-53
  4. A. A. Samarskii, P. P. Matus, P. N. Vabishchevich
    Pages 55-78
  5. A. A. Samarskii, P. P. Matus, P. N. Vabishchevich
    Pages 79-120
  6. A. A. Samarskii, P. P. Matus, P. N. Vabishchevich
    Pages 121-147
  7. A. A. Samarskii, P. P. Matus, P. N. Vabishchevich
    Pages 149-234
  8. A. A. Samarskii, P. P. Matus, P. N. Vabishchevich
    Pages 235-320
  9. A. A. Samarskii, P. P. Matus, P. N. Vabishchevich
    Pages 321-365
  10. Back Matter
    Pages 367-384

About this book

Introduction

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.

Keywords

Mathematica computational mathematics finite element method numerical method operator problem solving stability

Authors and affiliations

  • A. A. Samarskii
    • 1
  • P. P. Matus
    • 2
  • P. N. Vabishchevich
    • 1
  1. 1.Institute for Mathematical ModellingRussian Academy of SciencesMoscowRussia
  2. 2.Department of Numerical SimulationInstitute for MathematicsMinskBelarus

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-9874-3
  • Copyright Information Springer Science+Business Media B.V. 2002
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-6118-8
  • Online ISBN 978-94-015-9874-3
  • Buy this book on publisher's site