LEADER 04733nam 22006615 450 001 9910300545103321 005 20200704013112.0 010 $a3-319-78619-9 024 7 $a10.1007/978-3-319-78619-3 035 $a(CKB)3810000000358875 035 $a(DE-He213)978-3-319-78619-3 035 $a(MiAaPQ)EBC6314134 035 $a(PPN)22949062X 035 $a(EXLCZ)993810000000358875 100 $a20180621d2018 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aComputational Methods in Physics $eCompendium for Students /$fby Simon ?irca, Martin Horvat 205 $a2nd ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (XXIV, 880 p. 268 illus., 20 illus. in color.) 225 1 $aGraduate Texts in Physics,$x1868-4513 300 $aIncludes index. 311 $a3-319-78618-0 327 $aBasics of numerical analysis -- Solution of nonlinear equations -- Matrix methods -- Transformations of functions and signals -- Statistical description and modeling of data -- Modeling and analysis of time series -- Initial-value problems for ordinary differential equations -- Boundary-value problems for ordinary differential equations -- Difference methods for one-dimensional partial differential equations -- Difference methods for partial differential equations in more than one dim -- Spectral methods for partial differential equations -- Inverse methods. 330 $aThis book is intended to help advanced undergraduate, graduate, and postdoctoral students in their daily work by o?ering them a compendium of numerical methods. The choice of methods pays signi?cant attention to error estimates, stability and convergence issues, as well as optimization of program execution speeds. Numerous examples are given throughout the chapters, followed by comprehensive end-of-chapter problems with a more pronounced physics background, while less stress is given to the explanation of individual algorithms. The readers are encouraged to develop a certain amount of skepticism and scrutiny instead of blindly following readily available commercial tools. The second edition has been enriched by a chapter on inverse problems dealing with the solution of integral equations, inverse Sturm-Liouville problems, as well as retrospective and recovery problems for partial di?erential equations. The revised text now includes an introduction to sparse matrix methods, the solution of matrix equations, and pseudospectra of matrices; it discusses the sparse Fourier, non-uniform Fourier and discrete wavelet transformations, the basics of non-linear regression and the Kolmogorov-Smirnov test; it demonstrates the key concepts in solving sti? di?erential equations and the asymptotics of Sturm-Liouville eigenvalues and eigenfunctions. Among other updates, it also presents the techniques of state-space reconstruction, methods to calculate the matrix exponential, generate random permutations and compute stable derivatives. 410 0$aGraduate Texts in Physics,$x1868-4513 606 $aPhysics 606 $aChemistry, Physical and theoretical 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aComputer science$xMathematics 606 $aNumerical and Computational Physics, Simulation$3https://scigraph.springernature.com/ontologies/product-market-codes/P19021 606 $aTheoretical and Computational Chemistry$3https://scigraph.springernature.com/ontologies/product-market-codes/C25007 606 $aMathematical and Computational Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/T11006 606 $aComputational Science and Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/M14026 615 0$aPhysics. 615 0$aChemistry, Physical and theoretical. 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 0$aComputer science$xMathematics. 615 14$aNumerical and Computational Physics, Simulation. 615 24$aTheoretical and Computational Chemistry. 615 24$aMathematical and Computational Engineering. 615 24$aComputational Science and Engineering. 676 $a530.15 700 $a?irca$b Simon$4aut$4http://id.loc.gov/vocabulary/relators/aut$0479103 702 $aHorvat$b Martin$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300545103321 996 $aComputational Methods in Physics$92519509 997 $aUNINA