04055nam 22006612 450 991045425410332120151005020623.09780511995569electronic book0-511-99556-31-283-33039-397866133303901-139-13490-61-139-12986-41-139-13379-90-511-50423-30-511-50637-6(CKB)1000000000719115(EBL)424606(OCoLC)437110126(SSID)ssj0000360120(PQKBManifestationID)11244191(PQKBTitleCode)TC0000360120(PQKBWorkID)10326397(PQKB)11524875(UkCbUP)CR9780511995569(MiAaPQ)EBC424606(Au-PeEL)EBL424606(CaPaEBR)ebr10289172(CaONFJC)MIL333039(EXLCZ)99100000000071911520101018d2009|||| uy| 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierA first course in the numerical analysis of differential equations /Arieh Iserles[electronic resource]Second edition.Cambridge :Cambridge University Press,2009.1 online resource (xviii, 459 pages) digital, PDF file(s)Cambridge texts in applied mathematics ;44Title from publisher's bibliographic system (viewed on 05 Oct 2015).1-139-63656-1 Print version: 9780521734905 0-521-73490-8 Includes bibliographical references and index.Preface 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.Numerical 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.Cambridge texts in applied mathematics ;44.Differential equationsNumerical solutionsDifferential equationsNumerical solutions.518/.6Iserles A.21831UkCbUPUkCbUPBOOK9910454254103321First course in the numerical analysis of differential equations34050UNINA