Dòng Nội dung
1
An exponential function approach to parabolic equations / Chin-Yuan Lin
Hackensack, NJ : World Scientific, 2015
x, 163 pages. ; 23 cm.
Ký hiệu phân loại (DDC): 515.35
This volume is on initial-boundary value problems for parabolic partial differential equations of second order. It rewrites the problems as abstract Cauchy problems or evolution equations, and then solves them by the technique of elementary difference equations. Because of this, the volume assumes less background and provides an easy approach for readers to understand. Contents: Existence Theorems for Cauchy Problems; Existence Theorems for Evolution Equations (I); Linear Autonomous Parabolic Equations; Nonlinear Autonomous Parabolic Equations; Linear Non-autonomous Parabolic Equations; Nonlin
 Số bản sách: (1) Tài liệu số: (0)
2
Numerical differential equations : theory and technique, ode methods, finite differences, finite elements and collocation / John Loustau
New Jersey : World Scientific, 2016
xxi, 361 pages) : illustrations ; 25 cm.
Ký hiệu phân loại (DDC): 518.64
This text presents numerical differential equations to graduate (doctoral) students. It includes the three standard approaches to numerical PDE, FDM, FEM and CM, and the two most common time stepping techniques, FDM and Runge-Kutta. We present both the numerical technique and the supporting theory. The applied techniques include those that arise in the present literature. The supporting mathematical theory includes the general convergence theory. This material should be readily accessible to students with basic knowledge of mathematical analysis, Lebesgue measure and the basics of Hilbert spaces and Banach spaces. Nevertheless, we have made the book free standing in most respects. Most importantly, the terminology is introduced, explained and developed as needed. The examples presented are taken from multiple vital application areas including finance, aerospace, mathematical biology and fluid mechanics. The text may be used as the basis for several distinct lecture courses or as a reference. For instance, this text will support a general applications course or an FEM course with theory and applications. The presentation of material is empirically-based as more and more is demanded of the reader as we progress through the material. By the end of the text, the level of detail is reminiscent of journal articles. Indeed, it is our intention that this material be used to launch a research career in numerical PDE.
 Số bản sách: (3) Tài liệu số: (0)