## An Introduction to Scientific Computing: Twelve Computational Projects Solved with MATLABTeaching or learning numerical methods in applied mathematics cannot be conceived nowadays without numerical experimentation on computers. There is a vast literature devoted either to theoretical numerical methods or - merical programming of basic algorithms, but there are few texts o?ering a complete discussion of numerical issues involved in the solution of concrete and relatively complex problems. This book is an attempt to ?ll this need. It is our belief that advantages and drawbacks of a numerical method cannot be accounted for without one’s experiencing all the steps of scienti?c comp- ing, from physical and mathematical description of the problem to numerical formulation and programming and, ?nally, to critical discussion of numerical results. The book provides twelve computational projects aimed at numerically solving problems selected to cover a broad spectrum of applications, from ?uid mechanics, chemistry, elasticity, thermal science, computer-aided design, signal and image processing, etc. Even though the main volume of this text concerns the numerical analysis of computational methods and their imp- mentation, we have tried to start, when possible, from realistic problems of practical interest for researchers and engineers. For each project, an introductory record card summarizes the mathem- ical and numerical topics explained and the ?elds of application of the - proach. A level of di?culty, scaling from 1 to 3, is assigned to each project. |

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### Contents

1 | |

Application to Chemical | 33 |

Polynomial Approximation | 49 |

4 | 84 |

Solving a Differential Equation by a Spectral Method | 111 |

Multiresolution Analysis 127 | 126 |

Elastic Deformation of a Thin Plate | 151 |

Domain Decomposition Using a Schwarz Method | 165 |

Bézier Curves and Surfaces | 193 |

The Riemann Problem and Discontinuous | 213 |

Chapter References | 233 |

Chapter References | 250 |

12 | 251 |

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approximation array basis Bézier curve Bézier patch Bézier surface boundary conditions calculation Chap Chebyshev points components compute constant control points convergence corresponding Daubechies wavelet defined denote derivatives Differential Equations dipole Dirichlet discretization displayed in Fig error Exact sol exact solution example exercise is proposed expansion finite difference finite element method formula Fourier function f global grid Haar wavelet heat equation implement initial condition input integration interpolation interval iterations Kelvin–Helmholtz instability Lagrange Lagrange polynomials Laplacian Legendre linear system mathematical MATLAB matrix mesh multiresolution analysis nodes nonlinear numerical scheme numerical solution obtained parameters piecewise plot points xi polynomial polynomial interpolant procedure proposed in Sect quadrature reconstruction algorithm right-hand side right-hand-side function Runge–Kutta script shock tube Solution of Exercise solve the linear solver stability step subdomains temperature field tion tridiagonal u(tn un+1 values variables vector velocity Write a program