Iterative Splitting Methods for Differential Equations (Hardcover)

Juergen Geiser

  • 出版商: CRC
  • 出版日期: 2011-06-01
  • 售價: $2,880
  • 貴賓價: 9.5$2,736
  • 語言: 英文
  • 頁數: 320
  • 裝訂: Hardcover
  • ISBN: 1439869820
  • ISBN-13: 9781439869826
  • 相關分類: 數值分析 Numerical-analysis
  • 立即出貨 (庫存=1)

商品描述

Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources. It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave equations.

In the theoretical part of the book, the author discusses the main theorems and results of the stability and consistency analysis for ordinary differential equations. He then presents extensions of the iterative splitting methods to partial differential equations and spatial- and time-dependent differential equations.

The practical part of the text applies the methods to benchmark and real-life problems, such as waste disposal, elastics wave propagation, and complex flow phenomena. The book also examines the benefits of equation decomposition. It concludes with a discussion on several useful software packages, including r3t and FIDOS.

Covering a wide range of theoretical and practical issues in multiphysics and multiscale problems, this book explores the benefits of using iterative splitting schemes to solve physical problems. It illustrates how iterative operator splitting methods are excellent decomposition methods for obtaining higher-order accuracy.

商品描述(中文翻譯)

《迭代分割法求解微分方程》解釋了如何通過新穎的基於迭代的分割方法有效地使用計算和記憶資源來解決演化方程。它專注於抛物線和双曲線方程,包括對流-擴散-反應方程、熱方程和波動方程。

在書的理論部分,作者討論了普通微分方程穩定性和一致性分析的主要定理和結果。然後,他將迭代分割方法擴展到偏微分方程和空間和時間依賴的微分方程。

該書的實踐部分將這些方法應用於基準和實際問題,如廢物處理、彈性波傳播和複雜流動現象。該書還探討了方程分解的好處。最後,它討論了幾個有用的軟件包,包括r^3t和FIDOS。

涵蓋多物理和多尺度問題的廣泛理論和實踐問題,本書探討了使用迭代分割方案解決物理問題的好處。它說明了迭代算子分割方法如何成為獲得更高精度的優秀分解方法。