Traveling Wave Analysis of Partial Differential Equations: Numerical and Analytical Methods with Matlab and Maple (Hardcover)

Although the Partial Differential Equations (PDE) models that are now studied are usually beyond traditional mathematical analysis, the numerical methods that are being developed and used require testing and validation. This is often done with PDEs that have known, exact, analytical solutions. The development of analytical solutions is also an active area of research, with many advances being reported recently, particularly traveling wave solutions for nonlinear evolutionary PDEs. Thus, the current development of analytical solutions directly supports the development of numerical methods by providing a spectrum of test problems that can be used to evaluate numerical methods.

This book surveys some of these new developments in analytical and numerical methods, and relates the two through a series of PDE examples. The PDEs that have been selected are largely "named'' since they carry the names of their original contributors. These names usually signify that the PDEs are widely recognized and used in many application areas. The authors' intention is to provide a set of numerical and analytical methods based on the concept of a traveling wave, with a central feature of conversion of the PDEs to ODEs.

 The Matlab and Maple software will be available for download from this website shortly.

www.pdecomp.net

• Includes a spectrum of applications in science, engineering, applied mathematics


• Presents a combination of numerical and analytical methods


• Provides transportable computer codes in Matlab and Maple

儘管現在研究的偏微分方程（PDE）模型通常超出了傳統的數學分析範疇，但正在開發和使用的數值方法需要進行測試和驗證。這通常是通過具有已知、精確、解析解的PDE來完成的。解析解的發展也是一個活躍的研究領域，最近報導了許多進展，特別是非線性演化PDE的行波解。因此，目前解析解的發展通過提供一系列可用於評估數值方法的測試問題，直接支持數值方法的發展。

本書概述了一些這些新的解析和數值方法的發展，並通過一系列PDE示例將兩者相關聯。所選擇的PDE主要是“命名”的，因為它們帶有原始貢獻者的名字。這些名字通常表示這些PDE在許多應用領域中被廣泛認可和使用。作者的意圖是提供一套基於行波概念的數值和解析方法，其中的核心特點是將PDE轉換為ODE。

Matlab和Maple軟件將很快可以從本網站上下載。

www.pdecomp.net

- 包含了科學、工程、應用數學等多個應用領域的範譜
- 提供了數值和解析方法的結合
- 提供了Matlab和Maple的可移植計算機代碼