2nd. ed. - Springer, 2023. - 378 p. - ISBN: 3031350316.
This book demonstrates scientific computing by presenting
twelve computational projects in several disciplines including
Fluid Mechanics, Thermal Science, Computer Aided Design, Signal Processing and more. Each follows typical steps of scientific computing, from physical and mathematical description, to
numerical formulation and programming and critical discussion of results. The text teaches practical methods
not usually available in basic textbooks: numerical checking of accuracy, choice of boundary conditions, effective solving of linear systems, comparison to exact solutions and more. The final section of
each project contains the
solutions to proposed exercises and guides the reader in using the
MatLAB scripts available online.
Preface (2022).
Preface to the First Edition (2005).
Numerical Approximation of Model Partial Differential Equations.
Nonlinear Differential Equations: Application to Chemical Kinetics.
Fourier Approximation.
Polynomial Approximation.
Solving an Advection – Diffusion Equation by a Finite Element Method.
Solving a Differential Equation by a Legendre Spectral Method.
High-order finite difference methods.
Signal Processing: Multiresolution Analysis.
Elasticity: Elastic Deformation of a Thin Plate.
Domain Decomposition Using a Schwarz Method.
Geometrical Design: Bezier Curves and Surfaces.
Gas Dynamics: The Riemann Problem and Discontinuous Solutions: Application to the Shock
Tube Problem.
Optimization Applied to Model Fitting.
Thermal Engineering: Optimization of an Industrial Furnace.
Fluid Dynamics: Solving the 2D Navier – Stokes Equations.
Index.
Index of Programs.
True PDF