LEADER 04899nam 22006495 450 001 9910300558503321 005 20200704040929.0 010 $a3-319-42703-2 024 7 $a10.1007/978-3-319-42703-4 035 $a(CKB)4100000007110547 035 $a(MiAaPQ)EBC5568415 035 $a(DE-He213)978-3-319-42703-4 035 $a(PPN)231463103 035 $a(EXLCZ)994100000007110547 100 $a20181024d2018 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 13$aAn Introductory Guide to Computational Methods for the Solution of Physics Problems $eWith Emphasis on Spectral Methods /$fby George Rawitscher, Victo dos Santos Filho, Thiago Carvalho Peixoto 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (227 pages) 311 $a3-319-42702-4 327 $aDedication -- Preface -- Numerical Errors -- Methods -- Galerkin and Collocation Methods -- Convergence Theorems -- Chebyshev Polynomials -- The Integral Equation Corresponding to a Differential Equation -- Spectral Finite Element Method -- The Phase-Amplitude Representation of a Wave Function -- The Vibrating String -- Iteratively Calculated Eigenvalues -- Sturmian Functions -- Index. 330 $aThis monograph presents fundamental aspects of modern spectral and other computational methods, which are not generally taught in traditional courses. It emphasizes concepts as errors, convergence, stability, order and efficiency applied to the solution of physical problems. The spectral methods consist in expanding the function to be calculated into a set of appropriate basis functions (generally orthogonal polynomials) and the respective expansion coefficients are obtained via collocation equations. The main advantage of these methods is that they simultaneously take into account all available information, rather only the information available at a limited number of mesh points. They require more complicated matrix equations than those obtained in finite difference methods. However, the elegance, speed, and accuracy of the spectral methods more than compensates for any such drawbacks. During the course of the monograph, the authors examine the usually rapid convergence of the spectral expansions and the improved accuracy that results when nonequispaced support points are used, in contrast to the equispaced points used in finite difference methods. In particular, they demonstrate the enhanced accuracy obtained in the solution of integral equations. The monograph includes an informative introduction to old and new computational methods with numerous practical examples, while at the same time pointing out the errors that each of the available algorithms introduces into the specific solution. It is a valuable resource for undergraduate students as an introduction to the field and for graduate students wishing to compare the available computational methods. In addition, the work develops the criteria required for students to select the most suitable method to solve the particular scientific problem that they are confronting. 606 $aPhysics 606 $aSpectrum analysis 606 $aMicroscopy 606 $aSuperconductivity 606 $aSuperconductors 606 $aAtomic structure 606 $aMolecular structure 606 $aNumerical and Computational Physics, Simulation$3https://scigraph.springernature.com/ontologies/product-market-codes/P19021 606 $aSpectroscopy and Microscopy$3https://scigraph.springernature.com/ontologies/product-market-codes/P31090 606 $aStrongly Correlated Systems, Superconductivity$3https://scigraph.springernature.com/ontologies/product-market-codes/P25064 606 $aAtomic/Molecular Structure and Spectra$3https://scigraph.springernature.com/ontologies/product-market-codes/P24017 615 0$aPhysics. 615 0$aSpectrum analysis. 615 0$aMicroscopy. 615 0$aSuperconductivity. 615 0$aSuperconductors. 615 0$aAtomic structure. 615 0$aMolecular structure. 615 14$aNumerical and Computational Physics, Simulation. 615 24$aSpectroscopy and Microscopy. 615 24$aStrongly Correlated Systems, Superconductivity. 615 24$aAtomic/Molecular Structure and Spectra. 676 $a530.15 700 $aRawitscher$b George$4aut$4http://id.loc.gov/vocabulary/relators/aut$0833851 702 $ados Santos Filho$b Victo$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aPeixoto$b Thiago Carvalho$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910300558503321 996 $aAn Introductory Guide to Computational Methods for the Solution of Physics Problems$92497765 997 $aUNINA