书目名称 | Essential Partial Differential Equations |
副标题 | Analytical and Compu |
编辑 | David F. Griffiths,John W. Dold,David J. Silvester |
视频video | |
概述 | Analytical and computational approach to PDEs.Contains 300 exercises, all with full solutions, starred according to difficulty.One chapter dedicated to projects intended for individual or group study. |
丛书名称 | Springer Undergraduate Mathematics Series |
图书封面 |  |
描述 | .This volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs). It unifies an analytical and computational approach for these; the qualitative behaviour of solutions being established using classical concepts: maximum principles and energy methods. Notable inclusions are the treatment of irregularly shaped boundaries, polar coordinates and the use of flux-limiters when approximating hyperbolic conservation laws. The numerical analysis of difference schemes is rigorously developed using discrete maximum principles and discrete Fourier analysis. A novel feature is the inclusion of a chapter containing projects, intended for either individual or group study, that cover a range of topics such as parabolic smoothing, travelling waves, isospectral matrices, and the approximation of multidimensional advection–diffusion problems..The underlying theory is illustrated by numerous examples and there are around 300 exercises, designedto promote and test understanding. They are starred according to level of difficulty. Solutions to odd-numbered exercises are available to all readers while even-numbered solutions are available to authorised |
出版日期 | Textbook 2015 |
关键词 | Discrete Fourier Analysis; Energy Methods; Finite Difference Approximation; Maximum Principles; Method o |
版次 | 1 |
doi | https://doi.org/10.1007/978-3-319-22569-2 |
isbn_softcover | 978-3-319-22568-5 |
isbn_ebook | 978-3-319-22569-2Series ISSN 1615-2085 Series E-ISSN 2197-4144 |
issn_series | 1615-2085 |
copyright | Springer Nature Switzerland AG 2015 |