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New Difference Schemes for Partial Differential Equations

  • Allaberen Ashyralyev
  • Pavel E. Sobolevskii

Part of the Operator Theory: Advances and Applications book series (OT, volume 148)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Allaberen Ashyralyev, Pavel E. Sobolevskii
    Pages 1-10
  3. Allaberen Ashyralyev, Pavel E. Sobolevskii
    Pages 11-35
  4. Allaberen Ashyralyev, Pavel E. Sobolevskii
    Pages 37-98
  5. Allaberen Ashyralyev, Pavel E. Sobolevskii
    Pages 99-196
  6. Allaberen Ashyralyev, Pavel E. Sobolevskii
    Pages 197-311
  7. Allaberen Ashyralyev, Pavel E. Sobolevskii
    Pages 313-342
  8. Allaberen Ashyralyev, Pavel E. Sobolevskii
    Pages 343-392
  9. Allaberen Ashyralyev, Pavel E. Sobolevskii
    Pages 393-410
  10. Back Matter
    Pages 411-446

About this book

Introduction

The present monograph is devoted to the construction and investigation of the new high order of accuracy difference schemes of approximating the solutions of regular and singular perturbation boundary value problems for partial differential equations. The construction is based on the exact difference scheme and Taylor's decomposition on the two or three points. This approach permitted essentially to extend to a class of problems where the theory of difference methods is applicable. Namely, now it is possible to investigate the differential equations with variable coefficients and regular and singular perturbation boundary value problems. The investigation is based on new coercivity inequalities.

The book will be of value to professional mathematicians, as well as advanced students in the fields of numerical analysis, functional analysis, and ordinary and partial differential equations.

Keywords

Boundary value problem Numerische Analysis Operatortheorie Partielle Differentialgleichungen functional analysis hyperbolic equation numerical analysis partial differential equation

Authors and affiliations

  • Allaberen Ashyralyev
    • 1
    • 2
  • Pavel E. Sobolevskii
    • 3
  1. 1.Department of MathematicsFatih UniversityIstanbulTurkey
  2. 2.Department of MathematicsInternational Turkmen-Turkish UniversityAshgabatTurkmenistan
  3. 3.Department of MathematicsHebrew University of JerusalemJerusalemIsrael

Bibliographic information