LEADER 04142nam 22006852 450 001 9910782614003321 005 20220706165336.0 010 $a9780511995569$belectronic book 010 $a0-511-99556-3 010 $a1-283-33039-3 010 $a9786613330390 010 $a1-139-13490-6 010 $a1-139-12986-4 010 $a1-139-13379-9 010 $a0-511-50423-3 010 $a0-511-50637-6 035 $a(CKB)1000000000719115 035 $a(EBL)424606 035 $a(OCoLC)437110126 035 $a(SSID)ssj0000360120 035 $a(PQKBManifestationID)11244191 035 $a(PQKBTitleCode)TC0000360120 035 $a(PQKBWorkID)10326397 035 $a(PQKB)11524875 035 $a(UkCbUP)CR9780511995569 035 $a(MiAaPQ)EBC424606 035 $a(Au-PeEL)EBL424606 035 $a(CaPaEBR)ebr10289172 035 $a(CaONFJC)MIL333039 035 $a(PPN)261318233 035 $a(EXLCZ)991000000000719115 100 $a20101018d2009|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA first course in the numerical analysis of differential equations /$fArieh Iserles$b[electronic resource] 205 $aSecond edition. 210 1$aCambridge :$cCambridge University Press,$d2009. 215 $a1 online resource (xviii, 459 pages) $cdigital, PDF file(s) 225 1 $aCambridge texts in applied mathematics ;$v44 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 08$a1-139-63656-1 311 08$aPrint version: 9780521734905 0-521-73490-8 320 $aIncludes bibliographical references and index. 327 $aPreface to the first edition; Preface to the second edition; Flowchart of contents; Part I. Ordinary differential equations: 1. Euler's method and beyond; 2. Multistep methods; 3. Runge-Kutta methods; 4. Stiff equations; 5. Geometric numerical integration; 6. Error control; 7. Nonlinear algebraic systems; Part II. The Poisson equation: 8. Finite difference schemes; 9. The finite element method; 10. Spectral methods; 11. Gaussian elimination for sparse linear equations; 12. Classical iterative methods for sparse linear equations; 13. Multigrid techniques; 14. Conjugate gradients; 15. Fast Poisson solvers; Part III. Partial differential equations of evolution: 16. The diffusion equation; 17. Hyperbolic equations; Appendix. Bluffer's guide to useful mathematics: A.1. Linear algebra; A.2. Analysis; Bibliography; Index. 330 $aNumerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists and engineers it is a practical, applied subject, part of the standard repertoire of modelling techniques. For computer scientists it is a theory on the interplay of computer architecture and algorithms for real-number calculations. The tension between these standpoints is the driving force of this book, which presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The exposition maintains a balance between theoretical, algorithmic and applied aspects. This second edition has been extensively updated, and includes new chapters on emerging subject areas: geometric numerical integration, spectral methods and conjugate gradients. Other topics covered include multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; and a variety of algorithms to solve large, sparse algebraic systems. 410 0$aCambridge texts in applied mathematics ;$v44. 606 $aDifferential equations$xNumerical solutions 610 0$anumerisk analyse$adifferensialligninger 615 0$aDifferential equations$xNumerical solutions. 676 $a518/.6 700 $aIserles$b A.$021831 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910782614003321 996 $aFirst course in the numerical analysis of differential equations$934050 997 $aUNINA