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＜電子ブック＞
An Introduction to Scientific Computing : Fifteen Computational Projects Solved with MATLAB / by Ionut Danaila, Pascal Joly, Sidi Mahmoud Kaber, Marie Postel

版	2nd ed. 2023.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2023
本文言語	英語
大きさ	XVIII, 373 p. 137 illus., 110 illus. in color : online resource
著者標目	*Danaila, Ionut author Joly, Pascal author Kaber, Sidi Mahmoud author Postel, Marie author SpringerLink (Online service)
件　名	LCSH:Mathematics LCSH:Mathematics -- Data processing  全ての件名で検索 LCSH:Computational intelligence LCSH:Mathematical physics LCSH:Numerical analysis FREE:Applications of Mathematics FREE:Computational Mathematics and Numerical Analysis FREE:Computational Intelligence FREE:Theoretical, Mathematical and Computational Physics FREE:Numerical Analysis
一般注記	Numerical 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 This 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 HTTP:URL=https://doi.org/10.1007/978-3-031-35032-0

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