skip to content
Numerical methods for grid equations / 1. Direct methods. Preview this item
ClosePreview this item
Checking...

Numerical methods for grid equations / 1. Direct methods.

Author: Aleksandr A Samarskij
Publisher: Basel [u.a.] : Birkhäuser, 1989.
Edition/Format:   Print book : EnglishView all editions and formats
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

 

Find a copy online

Links to this item

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Aleksandr A Samarskij
ISBN: 0817622764 9780817622763 3764322780 9783764322786 3764322764 9783764322762
OCLC Number: 180494176
Description: XXXV, 242 S
Contents: 1 Direct Methods for Solving Difference Equations.- 1.1 Grid equations. Basic concepts.- 1.1.1 Grids and grid functions.- 1.1.2 Difference derivatives and various difference identities.- 1.1.3 Grid and difference equations.- 1.1.4 The Cauchy problem and boundary-value problems for difference equations.- 1.2 The general theory of linear difference equations.- 1.2.1 Properties of the solutions of homogeneous equations.- 1.2.2 Theorems about the solutions of linear equations.- 1.2.3 The method of variation of parameters.- 1.2.4 Examples.- 1.3 The solution of linear equations with constant coefficients.- 1.3.1 The characteristic equation. The simple-roots case.- 1.3.2 The multiple-root case.- 1.3.3 Examples.- 1.4 Second-order equations with constant coefficients.- 1.4.1 The general solution of a homogeneous equation.- 1.4.2 The Chebyshev polynomials.- 1.4.3 The general solution of a non-homogeneous equation.- 1.5 Eigenvalue difference problems.- 1.5.1 A boundary-value problem of the first kind.- 1.5.2 A boundary-value problem of the second kind.- 1.5.3 A mixed boundary-value problem.- 1.5.4 A periodic boundary-value problem.- 2 The Elimination Method.- 2.1 The elimination method for three-point equations.- 2.1.1 The algorithm.- 2.1.2 Two-sided elimination.- 2.1.3 Justification of the elimination method.- 2.1.4 Sample applications of the elimination method.- 2.2 Variants of the elimination method.- 2.2.1 The flow variant of the elimination method.- 2.2.2 The cyclic elimination metod.- 2.2.3 The elimination method for complicated systems.- 2.2.4 The non-monotonic elimination method.- 2.3 The elimination method for five-point equations.- 2.3.1 The monotone elimination algorithm.- 2.3.2 Justification of the method.- 2.3.3 A variant of non-monotonic elimination.- 2.4 The block-elimination method.- 2.4.1 Systems of vector equations.- 2.4.2 Elimination for three-point vector equations.- 2.4.3 Elimination for two-point vector equations.- 2.4.4 Orthogonal elimination for two-point vector equations.- 2.4.5 Elimination for three-point equations with constant coefficents.- 3 The Cyclic Reduction Method.- 3.1 Boundary-value problems for three-point vector equations.- 3.1.1 Statement of the boundary-value problems.- 3.1.2 A boundary-value problem of the first kind.- 3.1.3 Other boundary-value problems for difference equations.- 3.1.4 A high-accuracy Dirichlet difference problem.- 3.2 The cylic reduction method for a boundary-value problem of the first kind.- 3.2.1 The odd-even elimination process.- 3.2.2 Transformation of the right-hand side and inversion of the matrices.- 3.2.3 The algorithm for the method.- 3.2.4 The second algorithm of the method.- 3.3 Sample applications of the method.- 3.3.1 A Dirichlet difference problem for Poisson's equation in a rectangle.- 3.3.2 A high-accuracy Dirichlet difference problem.- 3.4 The cyclic reduction method for other boundary-value problems.- 3.4.1 A boundary-value problem of the second kind.- 3.4.2 A periodic problem.- 3.4.3 A boundary-value problem of the third kind.- 4 The Separation of Variables Method.- 4.1 The algorithm for the discrete Fourier transform.- 4.1.1 Statement of the problem.- 4.1.2 Expansion in sines and shifted sines.- 4.1.3 Expansion in cosines.- 4.1.4 Transforming a real-valued periodic grid function.- 4.1.5 Transforming a complex-valued periodic grid function.- 4.2 The solution of difference problems by the Fourier method.- 4.2.1 Eigenvalue difference problems for the Laplace operator in a rectangle.- 4.2.2 Poisson's equation in a rectangle; expansion in a double series.- 4.2.3 Expansion in a single series.- 4.3 The method of incomplete reduction.- 4.3.1 Combining the Fourier and reduction methods.- 4.3.2 The solution of boundary-value problems for Poisson's equation in a rectangle.- 4.3.3 A high-accuracy Dirichlet difference problem in a rectangle.- 4.4 The staircase algorithm and the reduction method for solving tridiagonal systems of equations.- 4.4.1 The staircase algorithm for the case of tridiagonal matrices with scalar elements.- 4.4.2 The staircase algorithm for the case of a block-tridiagonal matrix.- 4.4.3 Stability of the staircase algorithm.- 4.4.4 The reduction method for three-point scalar equations.
Responsibility: Aleksandr A. Samarskii ; Evgenii S. Nikolaev.

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/180494176> # Numerical methods for grid equations 1. Direct methods.
    a schema:Book, schema:CreativeWork ;
   library:oclcnum "180494176" ;
   library:placeOfPublication <http://id.loc.gov/vocabulary/countries/sz> ;
   library:placeOfPublication <http://experiment.worldcat.org/entity/work/data/235053632#Place/basel_u_a> ; # Basel u.a.
   schema:about <http://experiment.worldcat.org/entity/work/data/235053632#Topic/differenzengleichung> ; # Differenzengleichung
   schema:about <http://experiment.worldcat.org/entity/work/data/235053632#Topic/lineares_differenzengleichungssystem> ; # Lineares Differenzengleichungssystem
   schema:about <http://experiment.worldcat.org/entity/work/data/235053632#Topic/differentialgleichung> ; # Differentialgleichung
   schema:about <http://experiment.worldcat.org/entity/work/data/235053632#Topic/numerisches_verfahren> ; # Numerisches Verfahren
   schema:author <http://viaf.org/viaf/74374136> ; # Aleksandr A. Samarskij
   schema:bookFormat bgn:PrintBook ;
   schema:datePublished "1989" ;
   schema:exampleOfWork <http://worldcat.org/entity/work/id/235053632> ;
   schema:inLanguage "en" ;
   schema:name "Numerical methods for grid equations 1. Direct methods." ;
   schema:productID "180494176" ;
   schema:publication <http://www.worldcat.org/title/-/oclc/180494176#PublicationEvent/basel_u_a_birkhauser_1989> ;
   schema:publisher <http://experiment.worldcat.org/entity/work/data/235053632#Agent/birkhauser> ; # Birkhäuser
   schema:url <http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001196411&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA> ;
   schema:workExample <http://worldcat.org/isbn/9783764322762> ;
   schema:workExample <http://worldcat.org/isbn/9780817622763> ;
   schema:workExample <http://worldcat.org/isbn/9783764322786> ;
   wdrs:describedby <http://www.worldcat.org/title/-/oclc/180494176> ;
    .


Related Entities

<http://experiment.worldcat.org/entity/work/data/235053632#Topic/differentialgleichung> # Differentialgleichung
    a schema:Intangible ;
   schema:name "Differentialgleichung" ;
    .

<http://experiment.worldcat.org/entity/work/data/235053632#Topic/differenzengleichung> # Differenzengleichung
    a schema:Intangible ;
   schema:name "Differenzengleichung" ;
    .

<http://experiment.worldcat.org/entity/work/data/235053632#Topic/lineares_differenzengleichungssystem> # Lineares Differenzengleichungssystem
    a schema:Intangible ;
   schema:name "Lineares Differenzengleichungssystem" ;
    .

<http://experiment.worldcat.org/entity/work/data/235053632#Topic/numerisches_verfahren> # Numerisches Verfahren
    a schema:Intangible ;
   schema:name "Numerisches Verfahren" ;
    .

<http://viaf.org/viaf/74374136> # Aleksandr A. Samarskij
    a schema:Person ;
   schema:familyName "Samarskij" ;
   schema:givenName "Aleksandr A." ;
   schema:name "Aleksandr A. Samarskij" ;
    .

<http://worldcat.org/isbn/9780817622763>
    a schema:ProductModel ;
   schema:isbn "0817622764" ;
   schema:isbn "9780817622763" ;
    .

<http://worldcat.org/isbn/9783764322762>
    a schema:ProductModel ;
   schema:isbn "3764322764" ;
   schema:isbn "9783764322762" ;
    .

<http://worldcat.org/isbn/9783764322786>
    a schema:ProductModel ;
   schema:isbn "3764322780" ;
   schema:isbn "9783764322786" ;
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.