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Difference methods and their extrapolations

Author: Gurij Ivanovič Marčuk; V V Šajdurov
Publisher: New York ; Berlin : Springer-Verlag, cop. 1983.
Series: Applications of Mathematics, 19.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

The stimulus for the present work is the growing need for more accurate numerical methods. several orders The problem of finding the most efficient methods for the numerical solution of equations,  Read more...

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Genre/Form: Richardsonsche Extrapolation
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Gurij Ivanovič Marčuk; V V Šajdurov
ISBN: 0387907947 9780387907949 3540907947 9783540907947
OCLC Number: 632990633
Language Note: Aus d. Russ. übers.
Notes: Traduit de: Povyšenie tochnosti rešenij raznostnych schem.
Description: x, 334 p : fig ; 25 cm.
Contents: 1 General Properties.- 1.1. The Simplest Example.- 1.2. Expansion Theorems.- 1.3. Acceleration of Convergence.- 1.4. Correction by Higher-Order Differences.- 1.5. Various Extrapolation Methods.- 1.6. The Effects of Computational Errors.- 2 First-Order Ordinary Differential Equations.- 2.1. The Crank-Nicholson Scheme.- 2.2. Explicit Difference Schemes.- 2.3. The Splitting-Up Method for Systems of Equations.- 2.4. Equations with Singularities.- 3 The One-Dimensional Stationary Diffusion Equation.- 3.1. The Dirichlet Problem.- 3.2. Boundary-Value Problems of the Third Kind.- 3.3. Equations with Discontinuous Coefficients.- 3.4. The Sturm-Liouville Problem.- 3.5. Improving the Accuracy of the Finite Elements Method.- 3.6. The Quasilinear Problem.- 4 Elliptic Equations.- 4.1. The Statement of the Problem.- 4.2. Difference Methods for the Dirichlet Problem on a Domain with a Smooth Boundary.- 4.3. The Dirichlet Problem in a Rectangle.- 4.4. A Quasilinear Equation in a Triangular Region.- 4.5. On the Diffraction Problem.- 4.6. On the Separation of Singularities.- 5 Nonstationary Problems.- 5.1. The Simplest Type of Parabolic Equation.- 5.2. Increasing the Accuracy of the Splitting-Up Method.- 5.3. The Two-Dimensional Heat Equation.- 5.4. The Equation of Motion.- 6 Extrapolation for Algebraic Problems and Integral Equations.- 6.1. Regularization of a Singular System of Linear Algebraic Equations.- 6.2. Regularization of a System with a Selfadjoint Matrix.- 6.3. Extrapolation of Solutions Containing Boundary-Layer Functions.- 6.4. The Fredholm Equation of the Second Kind.- 6.5. The Volterra Equation of the Second Kind.- 6.6. The Volterra Equation of the First Kind.- 7 Appendix.- 7.1. Expansion of Difference Relations in the Mesh-Size.- 7.2. On the Solution of Some Special Systems of Equations.- 7.3. Some Results on the Lagrange Interpolation Polynomials.- List of Notation.
Series Title: Applications of Mathematics, 19.
Responsibility: G.I. Marchuk, V.V. Shaidurov.

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