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"Intended mainly for use as a reference manual, this third edition encompasses all the improvements of the newest version of the PLTMG software package. This updated version introduces several significant changes, including the following:The data structures defining the domain (triangulation and skeleton) have been simplified; more general boundary conditions are allowed.The internal data structure (triangle tree) has been replaced by a simple triangulation; the adaptive algorithms have been revised to use this simple data structure.The linear equations solvers are multigraph methods, which are simple ILU factorizations with strong connections to the hierarchical basis multigrid method.The graphics packages have been improved and now include expanded options.The test driver has a new X-Windows gui option."

"This book offers on the one hand a complete theory of Sobolev spaces, which are of fundamental importance for elliptic linear and non-linear differential equations, and explains on the other hand how the abstract methods of convex analysis can be combined with this theory to produce existence results for the solutions of non-linear elliptic boundary problems. The book also considers other kinds of functional spaces which are useful for treating variational problems such as the minimal surface problem."

"ABSTRACTThis paper will show a comparison between the Kepler, Maxwell and Pascal GPUarchitectures using CUDA-Fortran, with and without dynamic calls, to efficiently solve partialdifferential equations. The target is to show the possibility of using affordable hardware, such asthe GTX670, GTX970 and GTX1080 NVIDIA GPUs, which are commonly found in personaland portable computers, for scientific applications. For simplicity we consider a standardwave equation where we use a second order finite difference method for the spatial and timediscretizations to obtain the numerical solution. We found that, as we increase the spatialresolution of the domain we also increase the performance difference between the GPU and theCentral Processing Unit (CPU)"

"The book covers several topics of current interest in the field of nonlinear partial differential equations and their applications to the physics of continuous media and particle interactions. It treats the quasigeostrophic equation, integral diffusions, periodic Lorentz gas, Boltzmann equation, and critical dispersive nonlinear Schrödinger and wave equations. The book describes in a careful and expository manner several powerful methods from recent top research articles."

"This book deals with the numerical solution of differential equations, a very important branch of mathematics. Our aim is to give a practical and theoretical account of how to solve a large variety of differential equations, comprising ordinary differential equations, initial value problems and boundary value problems, differential algebraic equations, partial differential equations and delay differential equations. The solution of differential equations using R is the main focus of this book. Many examples are well-known test examples, used frequently in the field of numerical analysis."