## Numerical Analysis of Partial Differential EquationsA balanced guide to the essential techniques for solving elliptic partial differential equations The book presents the three main discretization methods of elliptic PDEs: finite difference, finite elements, and spectral methods. Each topic has its own devoted chapters and is discussed alongside additional key topics, including: -
The mathematical theory of elliptic PDEs -
Numerical linear algebra -
Time-dependent PDEs -
Multigrid and domain decomposition -
PDEs posed on infinite domains
The book concludes with a discussion of the methods for nonlinear problems, such as Newton's method, and addresses the importance of hands-on work to facilitate learning. Each chapter concludes with a set of exercises, including theoretical and programming problems, that allows readers to test their understanding of the presented theories and techniques. In addition, the book discusses important nonlinear problems in many fields of science and engineering, providing information as to how they can serve as computing projects across various disciplines. Requiring only a preliminary understanding of analysis, |

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### Contents

Finite Difference | 1 |

Mathematical Theory of Elliptic PDEs | 45 |

Finite Elements | 95 |

Numerical Linear Algebra | 169 |

Spectral Methods | 221 |

Evolutionary PDEs | 291 |

Multigrid | 345 |