Numerical Analysis Using R: Solutions to ODEs and PDEs

Graham W. Griffiths

  • 出版商: Cambridge
  • 出版日期: 2016-04-26
  • 售價: $3,510
  • 貴賓價: 9.5$3,335
  • 語言: 英文
  • 頁數: 632
  • 裝訂: Hardcover
  • ISBN: 1107115612
  • ISBN-13: 9781107115613
  • 相關分類: R 語言數值分析 Numerical-analysis
  • 海外代購書籍(需單獨結帳)

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商品描述

This book presents the latest numerical solutions to initial value problems and boundary value problems described by ODEs and PDEs. The author offers practical methods that can be adapted to solve wide ranges of problems and illustrates them in the increasingly popular open source computer language R, allowing integration with more statistically based methods. The book begins with standard techniques, followed by an overview of 'high resolution' flux limiters and WENO to solve problems with solutions exhibiting high gradient phenomena. Meshless methods using radial basis functions are then discussed in the context of scattered data interpolation and the solution of PDEs on irregular grids. Three detailed case studies demonstrate how numerical methods can be used to tackle very different complex problems. With its focus on practical solutions to real-world problems, this book will be useful to students and practitioners in all areas of science and engineering, especially those using R.

商品描述(中文翻譯)

本書介紹了最新的數值解法,用於描述由常微分方程和偏微分方程所描述的初值問題和邊界值問題。作者提供了實用的方法,可以適應解決各種問題,並在越來越受歡迎的開源計算機語言R中進行演示,以實現與更多基於統計的方法的集成。本書首先介紹了標準技術,然後概述了“高分辨率”通量限制器和WENO方法,用於解決具有高梯度現象的問題。接著,討論了使用基於徑向基函數的無網格方法,用於散點數據插值和在不規則網格上求解偏微分方程。三個詳細的案例研究展示了數值方法如何應用於解決非常不同的複雜問題。由於其專注於實際解決現實世界問題,本書對於所有科學和工程領域的學生和從業人員尤其是使用R的人將非常有用。