Computational Framework for the Finite Element Method in MATLAB and Python
by Pavel Sumets
Computational Framework for the Finite Element Method in MATLAB and Python aims to provide a programming framework for coding linear FEM using matrix-based MATLAB language and Python scripting language. It describes FEM algorithm implementation in the most generic formulation so that it is possible to apply this algorithm to as many application problems as possible. Readers can follow the step-by-step process of developing algorithms with clear explanations of its underlying mathematics and ho...
Solving Partial Differential Equations on Parallel Computers
by Jianping Zhu
The book, containing more than seventy exercises with detailed solutions, is well designed for a course both at the undergraduate and graduate levels.
Partial differential equations are used in mathematical models of a huge range of real-world phenomena, from electromagnetism to financial markets. This new edition of Applied PDEs contains many new sections and exercises Including, American options, transform methods, free surface flows, linear elasticity and complex characteristics.
Solutions of Nonlinear Differential Equations
by Lin Li and Shu-zhi Song
Partial Differential Equations: An Introduction, 3rd Edition covers the fundamental properties of partial differential equations (PDEs) and proven techniques useful in analyzing them. The text uses a broad approach to illustrate the rich diversity of phenomena such as vibrations of solids, fluid flow, molecular structure, photon and electron interactions, radiation of electromagnetic waves encompassed by this subject as well as the role PDEs play in modern mathematics, especially geometry and an...
Partial Differential Equations (Dover Books on Mathematics)
by Arthur David Snider
For courses in Partial Differential Equations taken by mathematics and engineering majors. An alternative to the obscure, jargon-heavy tomes on PDEs for math specialists and the cookbook, numerics-based "user manuals" (which provide little insight and questionable accuracy), this text presents full coverage of the analytic (and accurate) method for solving PDEs - in a manner that is both decipherable to engineering students and physically insightful for math students. The exposition is based on...
Frontiers in Differential Geometry, Partial Differential Equations and Mathematical Physics: In Memory of Gu Chaohao
This book is a collection of papers in memory of Gu Chaohao on the subjects of Differential Geometry, Partial Differential Equations and Mathematical Physics that Gu Chaohao made great contributions to with all his intelligence during his lifetime.All contributors to this book are close friends, colleagues and students of Gu Chaohao. They are all excellent experts among whom there are 9 members of the Chinese Academy of Sciences. Therefore this book will provide some important information on the...
Blow-up Theory for Elliptic PDEs in Riemannian Geometry (MN-45) (Mathematical Notes, #45)
by Olivier Druet, Emmanuel Hebey, and Frederic Robert
Elliptic equations of critical Sobolev growth have been the target of investigation for decades because they have proved to be of great importance in analysis, geometry, and physics. The equations studied here are of the well-known Yamabe type. They involve Schrodinger operators on the left hand side and a critical nonlinearity on the right hand side. A significant development in the study of such equations occurred in the 1980s. It was discovered that the sequence splits into a solution of the...
Observability and Mathematics (Advances in Applied Mathematics)
by Boris Khots
The author approaches an old classic problem - the existence of solutions of Navier-Stokes equations. The main objective is to model and derive of equation of continuity, Euler equation of fluid motion, energy flux equation, Navier-Stokes equations from the observer point of view and solve classic problem for this interpretation of fluid motion laws. If we have a piece of metal or a volume of liquid, the idea impresses itself upon us that it is divisible without limit, that any part of it, howe...
A Minicourse on Stochastic Partial Differential Equations (Lecture Notes in Mathematics, #1962)
by Robert Dalang, Davar Khoshnevisan, Carl Mueller, David Nualart, and Yimin Xiao
In May 2006, The University of Utah hosted an NSF-funded minicourse on stochastic partial differential equations. The goal of this minicourse was to introduce graduate students and recent Ph.D.s to various modern topics in stochastic PDEs, and to bring together several experts whose research is centered on the interface between Gaussian analysis, stochastic analysis, and stochastic partial differential equations. This monograph contains an up-to-date compilation of many of those lectures. Partic...
A Treatise on the Calculus of Finite Differences - Scholar's Choice Edition
by George Boole
Reaction-Diffusion Equations
Reaction-diffusion equations form a class of differential equations which in recent years have seen great steps forward both in the understanding of their analytical structure and in their application to a wide variety of scientific phenomena. This volume comprises a collection of articles on the theme of the theory and applications of reaction-diffusion equations. All the contributors are experts in their respective fields and together the articles will provide a coherent perspective to the cur...
Risk Prevention in Ophthalmology (Encyclopaedia of Mathematical Sciences; 30)
This book is concerned with functional methods (nonlinear semigroups of contractions, nonlinear m-accretive operators and variational techniques) in the theory of nonlinear partial differential equations of elliptic and parabolic type. In particular, applications to the existence theory of nonlinear parabolic equations, nonlinear Fokker-Planck equations, phase transition and free boundary problems are presented in details. Emphasis is put on functional methods in partial differential equations...