Showing results for "Complex Methods for Partial Differential Equations German"

Embark on an in-depth exploration of partial differential equations (PDEs) with "Advanced Partial Differential Equations." Our comprehensive guide provides a thorough overview of the theory, numerical methods, and practical applications of PDEs across various scientific and engineering fields. This resource is designed for both graduate-level students and professionals seeking to deepen their understanding of PDEs.We cover a wide range of topics, from classical PDEs and numerical m...

This book presents finite difference methods for three types of classical linear PDEs, three types of nonlinear PDEs and fractional PDEs. Specific topics cover two-point boundary value problems, elliptic equations, parabolic equations, hyperbolic equations, high-dimensional evolution equations, Schr\''{o}dinger equations, the Burgers' equation, the Korteweg-de Vries equation, and fractional diffusion-wave equations.The book strives to achieve:(a) Featured content. Thorough ...

This book presents a comprehensive and geometrical approach to solving partial differential equations (PDEs) on complex curved domains using orthonormal moving frames. Rooted in Élie Cartan’s classical theory but adapted for computational practicality, the framework aligns local basis vectors with the intrinsic geometry and anisotropy of the domain, enabling accurate and efficient discretization without requiring explicit metric tensors or Christoffel symbols. Topics include the constructi...

A new class of methods, termed "group explicit methods," is introduced in this text. Their applications to solve parabolic, hyperbolic and elliptic equations are outlined, and the advantages for their implementation on parallel computers clearly portrayed. Also included are the introductory and fundamental concepts from which the new methods are derived, and on which they are dependent. With the increasing advent of parallel computing into all aspects of computational mathematics, there is...

This book provides a comprehensive and systematic introduction to inverse problems for stochastic partial differential equations (SPDEs), with particular emphasis on stochastic parabolic and hyperbolic equations. It addresses both the unique challenges and new opportunities that arise in the stochastic setting. Key topics include inverse state problems (such as determining unknown initial conditions) and inverse source problems (identifying unknown source terms), with a focus on the mathem...

The monograph contains the description of physical models leading to some partial differential equations with applications. Both linear and nonlinear equations are considered. For each differential equation the main existing features are highlighted and complemented with examples and exercises. Preliminarly, a quick survey of the needed functional analytical tools is given: Sobolev spaces, the Lax-Milgram Theorem, the Galerkin method.

This volume is a selection of contributions offered by friends, collaborators, past students in memory of Enrico Magenes. The first part gives a wide historical perspective of Magenes' work in his 50-year mathematical career; the second part contains original research papers, and shows how ideas, methods, and techniques introduced by Magenes and his collaborators still have an impact on the current research in Mathematics.

This book presents a curated collection of recent research contributions in the field of nonlinear partial differential equations (PDEs), with an emphasis on hyperbolic problems. These equations are essential for modeling complex physical phenomena such as wave propagation, fluid dynamics, blood flow, and sediment transport. In many real-world applications, the governing equations are not purely hyperbolic but involve intricate interactions with elliptic or parabolic components.As ...

This popular text was created for a one-year undergraduate course or beginning graduate course in partial differential equations, including the elementary theory of complex variables. It employs a framework in which the general properties of partial differential equations, such as characteristics, domains of independence, and maximum principles, can be clearly seen. The only prerequisite is a good course in calculus.Incorporating many of the techniques of applied mathematics, the bo...

Partial Differential Equations and Applications: A Bridge for Students and Researchers in Applied Sciences offers a unique approach to this key subject by connecting mathematical principles to the latest research advances in select topics. Beginning with very elementary PDEs, such as classical heat equations, wave equations and Laplace equations, the book focuses on concrete examples. It gives students basic skills and techniques to find explicit solutions for partial differential equation...

This third and final volume in our Mathematics for Engineers series serves as a companion text to the third-semester mathematics preliminaries for students and lecturers in electrical engineering and other engineering disciplines.Ordinary and partially differential equations play a central role in graduate engineering courses. This topic is one of the main focus of the third volume. In addition to describing engineering problems using differential equations, we analyze signals prod...

The aim of this book is to quickly elevate students to a proficiency level where they can solve linear and nonlinear partial differential equations using state-of-the-art numerical methods. It covers numerous topics typically absent in introductory texts on ODEs and PDEs, including:Computing solutions to chaotic dynamical systems with TRBDF2Simulating the nonlinear diffusion equation with TRBDF2Applying Newton’s method and GMRES to the nonlinear Laplace eq...