The known generalization of the Poincare-Lighthill perturbation method of strained coordinates are investigated and compared. Some new conditions for its applicability are conjectured and some of its limitations are shown. (Author)
|Statement||by Craig Comstock|
|Contributions||Naval Postgraduate School (U.S.)|
|The Physical Object|
|Pagination||30 p. :|
|Number of Pages||30|
This chapter discusses the Poincaré–Lighthill–Kuo method. Lighthill applied his method to problems involving partial differential equations when the zeroth order solution is obtained from a reduced linear equation of equal order as the exact by: 7. Download Citation | Poincare-Lighthill-Kuo method and symbolic computation | This paper elucidates the effectiveness of combining the Poincare-Lighthill-Kuo method (PLK method, for short) and. Craig Comstock. () The Poincaré–Lighthill Perturbation Technique and Its Generalizations. SIAM Review , Abstract | PDF ( KB) () A Special Topics Course in Perturbation Cited by: It is a great book and I highly recommend it! The title accurately describes the text however: the book provides only a first look at these topics. It is a great book for those like me who would like to get an idea about what perturbation theory is good for, but it is not appropriate for those looking for a thorough s: 7.
Perturbation theory is a powerful tool for solving a wide variety of problems in applied mathematics, a tool particularly useful in quantum mechanics and chemistry. Although most books on these subjects include a section offering an overview of perturbation theory, few, if any, take a practical approach that addresses its actual implementation. The Poincaré–Lighthill perturbation technique and its generalizations. SIAM Rev., 14(3)–, zbMATH MathSciNet Google Scholar Singular perturbation techniques: a comparison of the method of matched asymptotic expansions with that of multiple scales. Buy this book on publisher's site; Personalised recommendations. Cite. The monograph Perturbation Methods in Applied Mathematics, Cole , considered singular perturbations in a broad applied math setting, where both the development of the underlying techniques and significant and diverse applications were included. The book approaches matching using intermediate limits and presumes a corresponding overlap of. It may be noticed that the out-of-plane perturbation equations () and () in the extensible case are identical to those for an inextensible pipe, equations () and (), provided that η o 2 = 0 and that the steady pressure-tension effects are taken into account. As established earlier in this section, the former condition is satisfied if the pipe initially lies in a vertical plane.
The head-on collision between two cylindrical/spherical ion acoustic solitary waves (IASWs) in un-magnetized plasmas comprising inertial ions and q-non-extensive electrons and positrons is. Throughout the book, the style is clear and elegant. this book can be highly recommended to anybody who works in this area." (Adina Luminita Sasu, Zentralblatt MATH, Vol. (23), ) "More precisely, as correctly described in the title, [BA] concentrates on the perturbation of positive semigroups and its applications to birth and death. In this book the author presents the theory and techniques underlying perturbation methods in a manner that will make the book widely appealing to readers in a broad range of disciplines. Methods of algebraic equations, asymptotic expansions, integrals, PDEs, strained coordinates, and multiple scales are illustrated by copious use of examples drawn from many areas of mathematics and physics/5(2). The renormalized Poincaré-Lighthill perturbation theory (Thesis ) applied to the method of Shoot and Fit for systems of nonlinear ODEs with 2-point boundary conditions, widens the circle of convergence (IJAA 3, , ).