Line Integral Methods For Conservative Problems PDF Download
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Author | : Luigi Brugnano |
Publisher | : CRC Press |
Total Pages | : 239 |
Release | : 2016-03-09 |
Genre | : Mathematics |
ISBN | : 1482263858 |
Download Line Integral Methods for Conservative Problems Book in PDF, ePub and Kindle
Line Integral Methods for Conservative Problems explains the numerical solution of differential equations within the framework of geometric integration, a branch of numerical analysis that devises numerical methods able to reproduce (in the discrete solution) relevant geometric properties of the continuous vector field. The book focuses on a large
Author | : Luigi Brugnano |
Publisher | : MDPI |
Total Pages | : 306 |
Release | : 2019-06-20 |
Genre | : Juvenile Nonfiction |
ISBN | : 3038976660 |
Download Advanced Numerical Methods in Applied Sciences Book in PDF, ePub and Kindle
The use of scientific computing tools is currently customary for solving problems at several complexity levels in Applied Sciences. The great need for reliable software in the scientific community conveys a continuous stimulus to develop new and better performing numerical methods that are able to grasp the particular features of the problem at hand. This has been the case for many different settings of numerical analysis, and this Special Issue aims at covering some important developments in various areas of application.
Author | : Raffaele D'Ambrosio |
Publisher | : Springer Nature |
Total Pages | : 391 |
Release | : 2023-09-26 |
Genre | : Mathematics |
ISBN | : 3031313437 |
Download Numerical Approximation of Ordinary Differential Problems Book in PDF, ePub and Kindle
This book is focused on the numerical discretization of ordinary differential equations (ODEs), under several perspectives. The attention is first conveyed to providing accurate numerical solutions of deterministic problems. Then, the presentation moves to a more modern vision of numerical approximation, oriented to reproducing qualitative properties of the continuous problem along the discretized dynamics over long times. The book finally performs some steps in the direction of stochastic differential equations (SDEs), with the intention of offering useful tools to generalize the techniques introduced for the numerical approximation of ODEs to the stochastic case, as well as of presenting numerical issues natively introduced for SDEs. The book is the result of an intense teaching experience as well as of the research carried out in the last decade by the author. It is both intended for students and instructors: for the students, this book is comprehensive and rather self-contained; for the instructors, there is material for one or more monographic courses on ODEs and related topics. In this respect, the book can be followed in its designed path and includes motivational aspects, historical background, examples and a software programs, implemented in Matlab, that can be useful for the laboratory part of a course on numerical ODEs/SDEs. The book also contains the portraits of several pioneers in the numerical discretization of differential problems, useful to provide a framework to understand their contributes in the presented fields. Last, but not least, rigor joins readability in the book.
Author | : Jiguang Sun |
Publisher | : CRC Press |
Total Pages | : 368 |
Release | : 2016-08-19 |
Genre | : Mathematics |
ISBN | : 1482254654 |
Download Finite Element Methods for Eigenvalue Problems Book in PDF, ePub and Kindle
This book covers finite element methods for several typical eigenvalues that arise from science and engineering. Both theory and implementation are covered in depth at the graduate level. The background for typical eigenvalue problems is included along with functional analysis tools, finite element discretization methods, convergence analysis, techniques for matrix evaluation problems, and computer implementation. The book also presents new methods, such as the discontinuous Galerkin method, and new problems, such as the transmission eigenvalue problem.
Author | : Willi Freeden |
Publisher | : CRC Press |
Total Pages | : 513 |
Release | : 2017-11-22 |
Genre | : Mathematics |
ISBN | : 1351764756 |
Download Integration and Cubature Methods Book in PDF, ePub and Kindle
In industry and economics, the most common solutions of partial differential equations involving multivariate numerical integration over cuboids include techniques of iterated one-dimensional approximate integration. In geosciences, however, the integrals are extended over potato-like volumes (such as the ball, ellipsoid, geoid, or the Earth) and their boundary surfaces which require specific multi-variate approximate integration methods. Integration and Cubature Methods: A Geomathematically Oriented Course provides a basic foundation for students, researchers, and practitioners interested in precisely these areas, as well as breaking new ground in integration and cubature in geomathematics.
Author | : Yaroslav D. Sergeyev |
Publisher | : Luigi Pellegrini Editore |
Total Pages | : 153 |
Release | : 2013-06-27 |
Genre | : Mathematics |
ISBN | : 8868220334 |
Download Proceedings of the international conference "“NUMERICAL COMPUTATIONS: THEORY AND ALGORITHMS” Book in PDF, ePub and Kindle
This book contains Proceedings of the International Conference and Summer School NUMTA-2013 “Numerical Computations: Theory and Algorithms”. The Conference is organized jointly by the University of Calabria, Italy, and by the N.I. Lobachevsky State University of Nizhni Novgorod, Russia in cooperation with the Society for Industrial and Applied Mathematics (SIAM), USA. The goal of the Conference is to create a multidisciplinary round table for an open discussion on numerical modeling nature by using traditional and emerging computational paradigms. The Conference discusses all aspects of numerical computations and modeling from foundations and philosophy to advanced numerical techniques. New technological challenges and fundamental ideas from theoretical computer science, linguistic, logic, set theory, and philosophy meet requirements and new fresh applications from physics, chemistry, biology, and economy.
Author | : Daniele Bertaccini |
Publisher | : CRC Press |
Total Pages | : 375 |
Release | : 2018-02-19 |
Genre | : Mathematics |
ISBN | : 1498764177 |
Download Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications Book in PDF, ePub and Kindle
This book describes, in a basic way, the most useful and effective iterative solvers and appropriate preconditioning techniques for some of the most important classes of large and sparse linear systems. The solution of large and sparse linear systems is the most time-consuming part for most of the scientific computing simulations. Indeed, mathematical models become more and more accurate by including a greater volume of data, but this requires the solution of larger and harder algebraic systems. In recent years, research has focused on the efficient solution of large sparse and/or structured systems generated by the discretization of numerical models by using iterative solvers.
Author | : Xinyuan Wu |
Publisher | : Springer Nature |
Total Pages | : 507 |
Release | : 2021-09-28 |
Genre | : Mathematics |
ISBN | : 981160147X |
Download Geometric Integrators for Differential Equations with Highly Oscillatory Solutions Book in PDF, ePub and Kindle
The idea of structure-preserving algorithms appeared in the 1980's. The new paradigm brought many innovative changes. The new paradigm wanted to identify the long-time behaviour of the solutions or the existence of conservation laws or some other qualitative feature of the dynamics. Another area that has kept growing in importance within Geometric Numerical Integration is the study of highly-oscillatory problems: problems where the solutions are periodic or quasiperiodic and have to be studied in time intervals that include an extremely large number of periods. As is known, these equations cannot be solved efficiently using conventional methods. A further study of novel geometric integrators has become increasingly important in recent years. The objective of this monograph is to explore further geometric integrators for highly oscillatory problems that can be formulated as systems of ordinary and partial differential equations. Facing challenging scientific computational problems, this book presents some new perspectives of the subject matter based on theoretical derivations and mathematical analysis, and provides high-performance numerical simulations. In order to show the long-time numerical behaviour of the simulation, all the integrators presented in this monograph have been tested and verified on highly oscillatory systems from a wide range of applications in the field of science and engineering. They are more efficient than existing schemes in the literature for differential equations that have highly oscillatory solutions. This book is useful to researchers, teachers, students and engineers who are interested in Geometric Integrators and their long-time behaviour analysis for differential equations with highly oscillatory solutions.
Author | : Irina V. Melnikova |
Publisher | : CRC Press |
Total Pages | : 232 |
Release | : 2018-09-03 |
Genre | : Mathematics |
ISBN | : 1315360268 |
Download Stochastic Cauchy Problems in Infinite Dimensions Book in PDF, ePub and Kindle
Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions presents stochastic differential equations for random processes with values in Hilbert spaces. Accessible to non-specialists, the book explores how modern semi-group and distribution methods relate to the methods of infinite-dimensional stochastic analysis. It also shows how the idea of regularization in a broad sense pervades all these methods and is useful for numerical realization and applications of the theory. The book presents generalized solutions to the Cauchy problem in its initial form with white noise processes in spaces of distributions. It also covers the "classical" approach to stochastic problems involving the solution of corresponding integral equations. The first part of the text gives a self-contained introduction to modern semi-group and abstract distribution methods for solving the homogeneous (deterministic) Cauchy problem. In the second part, the author solves stochastic problems using semi-group and distribution methods as well as the methods of infinite-dimensional stochastic analysis.
Author | : Victor H. Moll |
Publisher | : CRC Press |
Total Pages | : 272 |
Release | : 2015-10-27 |
Genre | : Mathematics |
ISBN | : 1482256541 |
Download Special Integrals of Gradshteyn and Ryzhik Book in PDF, ePub and Kindle
A Guide to the Evaluation of IntegralsSpecial Integrals of Gradshetyn and Ryzhik: the Proofs provides self-contained proofs of a variety of entries in the frequently used table of integrals by I.S. Gradshteyn and I.M. Ryzhik. The book gives the most elementary arguments possible and uses Mathematica to verify the formulas. You will discover the bea