Implicit Explicit Methods For Evolutionary Partial Differential Equations
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Implicit Explicit Methods For Evolutionary Partial Differential Equations
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Author : Sebastiano Boscarino
language : en
Publisher: SIAM
Release Date : 2024-12-12
Implicit Explicit Methods For Evolutionary Partial Differential Equations written by Sebastiano Boscarino and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-12 with Mathematics categories.
Implicit-explicit (IMEX) time discretization methods have proven to be highly effective for the numerical solution of a wide class of evolutionary partial differential equations (PDEs) across various contexts. These methods have become mainstream for solving evolutionary PDEs, particularly in the fields of hyperbolic and kinetic equations. The first book on the subject, Implicit-Explicit Methods for Evolutionary Partial Differential Equations provides an in-depth yet accessible approach. The authors summarize and illustrate the construction, analysis, and application of IMEX methods using examples, test cases, and implementation details; guide readers through the various methods and teach them how to select and use the one most appropriate for their needs; and demonstrate how to identify stiff terms and effectively implement high-order methods in time for a variety of systems of PDEs. Readers interested in learning modern techniques for the effective numerical solution of evolutionary PDEs with multiple time scales will find in this book a unified, compact, and accessible treatment. This book is intended for applied mathematicians, scientists, and engineers who use or are interested in learning about IMEX schemes. Readers should have some background in numerical methods for ODE systems and basic finite difference and finite volume discretization of evolutionary PDEs, along with a basic understanding of the relevant mathematical models. The book is suitable for students who have had a basic course in numerical analysis and are familiar with partial differential equations.
Numerical Methods For Evolutionary Differential Equations
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Author : Uri M. Ascher
language : en
Publisher: SIAM
Release Date : 2008-01-01
Numerical Methods For Evolutionary Differential Equations written by Uri M. Ascher and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.
Methods for the numerical simulation of dynamic mathematical models have been the focus of intensive research for well over 60 years, and the demand for better and more efficient methods has grown as the range of applications has increased. Mathematical models involving evolutionary partial differential equations (PDEs) as well as ordinary differential equations (ODEs) arise in diverse applications such as fluid flow, image processing and computer vision, physics-based animation, mechanical systems, relativity, earth sciences, and mathematical finance. This textbook develops, analyzes, and applies numerical methods for evolutionary, or time-dependent, differential problems. Both PDEs and ODEs are discussed from a unified viewpoint. The author emphasizes finite difference and finite volume methods, specifically their principled derivation, stability, accuracy, efficient implementation, and practical performance in various fields of science and engineering. Smooth and nonsmooth solutions for hyperbolic PDEs, parabolic-type PDEs, and initial value ODEs are treated, and a practical introduction to geometric integration methods is included as well. Audience: suitable for researchers and graduate students from a variety of fields including computer science, applied mathematics, physics, earth and ocean sciences, and various engineering disciplines. Researchers who simulate processes that are modeled by evolutionary differential equations will find material on the principles underlying the appropriate method to use and the pitfalls that accompany each method.
Computational Mechanics And Applied Mathematics Perspectives From Young Scholars
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Author : Francesco Marmo
language : en
Publisher: Springer Nature
Release Date : 2025-03-27
Computational Mechanics And Applied Mathematics Perspectives From Young Scholars written by Francesco Marmo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-27 with Mathematics categories.
This book collects the latest advances and innovations in the field of applied mathematics and computational mechanics, as presented at the 2nd Workshop GIMC SIMAI YOUNG, held in Naples, Italy, on July 10–12, 2024. The workshop was the joint effort of Computational Mechanics Group of the Italian Association of Theoretical and Applied Mechanics -AIMETA (GIMC) and Italian Society of Applied and Industrial Mathematics (SIMAI) and was meant to highlight the works of young researchers in the field. Topics include mathematical models for socio-epidemiological dynamics, efficient numerical methods for evolutionary PDEs, multi-scale approaches and machine learning techniques in material modelling, nonlinear material behaviour, computational methods for shells and spatial structures, assessment, monitoring, and design of masonry structures, particles in numerical simulations, non-Newtonian complex fluids, mathematical modelling in mechanobiology and oncology, mechanics of biological systems and bioinspired materials, computational approaches for complex dynamical systems, optimization methods for classical and data-driven approaches. The contributions, which were selected by means of a rigorous peer-review process, present a wealth of exciting ideas that will open novel research directions and foster multidisciplinary collaboration.
Additive Operator Difference Schemes
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Author : Petr N. Vabishchevich
language : en
Publisher: Walter de Gruyter
Release Date : 2013-11-27
Additive Operator Difference Schemes written by Petr N. Vabishchevich and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Mathematics categories.
Applied mathematical modeling is concerned with solving unsteady problems. Splitting schemes are attributed to the transition from a complex problem to a chain of simpler problems. This book shows how to construct additive difference schemes (splitting schemes) to solve approximately unsteady multi-dimensional problems for PDEs. Two classes of schemes are highlighted: methods of splitting with respect to spatial variables (alternating direction methods) and schemes of splitting into physical processes. Also regionally additive schemes (domain decomposition methods) and unconditionally stable additive schemes of multi-component splitting are considered for evolutionary equations of first and second order as well as for systems of equations. The book is written for specialists in computational mathematics and mathematical modeling. All topics are presented in a clear and accessible manner.
High Order Nonlinear Numerical Schemes For Evolutionary Pdes
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Author : Rémi Abgrall
language : en
Publisher: Springer
Release Date : 2014-05-19
High Order Nonlinear Numerical Schemes For Evolutionary Pdes written by Rémi Abgrall and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-19 with Mathematics categories.
This book collects papers presented during the European Workshop on High Order Nonlinear Numerical Methods for Evolutionary PDEs (HONOM 2013) that was held at INRIA Bordeaux Sud-Ouest, Talence, France in March, 2013. The central topic is high order methods for compressible fluid dynamics. In the workshop, and in this proceedings, greater emphasis is placed on the numerical than the theoretical aspects of this scientific field. The range of topics is broad, extending through algorithm design, accuracy, large scale computing, complex geometries, discontinuous Galerkin, finite element methods, Lagrangian hydrodynamics, finite difference methods and applications and uncertainty quantification. These techniques find practical applications in such fields as fluid mechanics, magnetohydrodynamics, nonlinear solid mechanics, and others for which genuinely nonlinear methods are needed.
Scientific And Technical Aerospace Reports
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Author :
language : en
Publisher:
Release Date : 1988
Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Aeronautics categories.
Advances In Differential Evolution
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Author : Uday K. Chakraborty
language : en
Publisher: Springer
Release Date : 2008-09-08
Advances In Differential Evolution written by Uday K. Chakraborty and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-08 with Computers categories.
Differential evolution is arguably one of the hottest topics in today's computational intelligence research. This book seeks to present a comprehensive study of the state of the art in this technology and also directions for future research. The fourteen chapters of this book have been written by leading experts in the area. The first seven chapters focus on algorithm design, while the last seven describe real-world applications. Chapter 1 introduces the basic differential evolution (DE) algorithm and presents a broad overview of the field. Chapter 2 presents a new, rotationally invariant DE algorithm. The role of self-adaptive control parameters in DE is investigated in Chapter 3. Chapters 4 and 5 address constrained optimization; the former develops suitable stopping conditions for the DE run, and the latter presents an improved DE algorithm for problems with very small feasible regions. A novel DE algorithm, based on the concept of "opposite" points, is the topic of Chapter 6. Chapter 7 provides a survey of multi-objective differential evolution algorithms. A review of the major application areas of differential evolution is presented in Chapter 8. Chapter 9 discusses the application of differential evolution in two important areas of applied electromagnetics. Chapters 10 and 11 focus on applications of hybrid DE algorithms to problems in power system optimization. Chapter 12 applies the DE algorithm to computer chess. The use of DE to solve a problem in bioprocess engineering is discussed in Chapter 13. Chapter 14 describes the application of hybrid differential evolution to a problem in control engineering.
Evolutionary Computation Machine Learning And Data Mining In Bioinformatics
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Author : Elena Marchiori
language : en
Publisher: Springer
Release Date : 2007-06-21
Evolutionary Computation Machine Learning And Data Mining In Bioinformatics written by Elena Marchiori and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-21 with Computers categories.
This book constitutes the refereed proceedings of the 5th European Conference on Evolutionary Computation, Machine Learning and Data Mining in Bioinformatics, EvoBIO 2007, held in Valencia, Spain, April 2007. Coverage brings together experts in computer science with experts in bioinformatics and the biological sciences. It presents contributions on fundamental and theoretical issues along with papers dealing with different applications areas.
Applied Mechanics Reviews
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Author :
language : en
Publisher:
Release Date : 1985
Applied Mechanics Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mechanics, Applied categories.
Numerical Methods For Evolutionary Differential Equations
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Author : Uri M. Ascher
language : en
Publisher: SIAM
Release Date : 2008-09-04
Numerical Methods For Evolutionary Differential Equations written by Uri M. Ascher and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-04 with Mathematics categories.
Develops, analyses, and applies numerical methods for evolutionary, or time-dependent, differential problems.