LEADER 04908nam 22007455 450 001 9910760268503321 005 20240703111234.0 010 $a3-031-35032-4 024 7 $a10.1007/978-3-031-35032-0 035 $a(CKB)28779884200041 035 $a(MiAaPQ)EBC30870427 035 $a(Au-PeEL)EBL30870427 035 $a(DE-He213)978-3-031-35032-0 035 $a(EXLCZ)9928779884200041 100 $a20231106d2023 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 13$aAn Introduction to Scientific Computing $eFifteen Computational Projects Solved with MATLAB /$fby Ionut Danaila, Pascal Joly, Sidi Mahmoud Kaber, Marie Postel 205 $a2nd ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023. 215 $a1 online resource (379 pages) 311 08$a9783031350313 327 $aNumerical Approximation of Model Partial Differential Equations -- Nonlinear Differential Equations: Application to Chemical Kinetics -- Polynomial Approximation -- Solving an Advection-Diffusion Equation by a Finite Element Method -- Solving a Differential Equation by a Spectral Method -- Signal Processing: Multiresolution Analysis -- Elasticity: Elastic Deformation of a Thin Plate -- Domain Decomposition Using a Schwarz Method -- Geometrical Design: Bézier Curves and Surfaces -- Gas Dynamics: The Riemann Problem and Discontinuous Solutions: Application to the Shock Tube Problem -- Thermal Engineering: Optimization of an Industrial Furnace -- Fluid Dynamics: Solving the Two-Dimensional Navier-Stokes Equations. 330 $aThis book provides fifteen computational projects aimed at numerically solving problems from a broad range of applications including Fluid Mechanics, Chemistry, Elasticity, Thermal Science, Computer Aided Design, Signal and Image Processing. For each project the reader is guided through the typical steps of scientific computing from physical and mathematical description of the problem to numerical formulation and programming and finally to critical discussion of numerical results. Considerable emphasis is placed on practical issues of computational methods. The last section of each project contains the solutions to all proposed exercises and guides the reader in using the MATLAB scripts. The mathematical framework provides a basic foundation in numerical analysis of partial differential equations and main discretization techniques, such as finite differences, finite elements, spectral methods and wavelets. The book is primarily intended as a graduate-level text in applied mathematics, but it may also be used by students in engineering or physical sciences. It will also be a useful reference for researchers and practicing engineers. The second edition builds upon its earlier material (revised and updated) with three all-new chapters intended to reinforce the presentation of mathematical aspects on numerical methods: Fourier approximation, high-order finite difference methods, and basic tools for numerical optimization. Corresponding new applications and programs concern spectral Fourier methods to solve ordinary differential equations, finite difference methods up to sixth-order to solve boundary value problems and, finally, optimization strategies to fit parameters of an epidemiological model. 606 $aMathematics 606 $aMathematics$xData processing 606 $aComputational intelligence 606 $aMathematical physics 606 $aNumerical analysis 606 $aApplications of Mathematics 606 $aComputational Mathematics and Numerical Analysis 606 $aComputational Intelligence 606 $aTheoretical, Mathematical and Computational Physics 606 $aNumerical Analysis 606 $aAnàlisi numèrica$2thub 606 $aProcessament de dades$2thub 608 $aLlibres electrònics$2thub 615 0$aMathematics. 615 0$aMathematics$xData processing. 615 0$aComputational intelligence. 615 0$aMathematical physics. 615 0$aNumerical analysis. 615 14$aApplications of Mathematics. 615 24$aComputational Mathematics and Numerical Analysis. 615 24$aComputational Intelligence. 615 24$aTheoretical, Mathematical and Computational Physics. 615 24$aNumerical Analysis. 615 7$aAnàlisi numèrica. 615 7$aProcessament de dades 676 $a620.00151 676 $a620.00151 700 $aDanaila$b Ionut$0739188 701 $aJoly$b Pascal$01438300 701 $aKaber$b Sidi Mahmoud$0311995 701 $aPostel$b Marie$01438301 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910760268503321 996 $aAn Introduction to Scientific Computing$93599592 997 $aUNINA