Formal Algorithmic Elimination For Pdes

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Formal Algorithmic Elimination for PDEs

Daniel Robertz
Formal Algorithmic Elimination for PDEs Book PDF

Author : Daniel Robertz
Publisher : Springer
Page : 291 pages
File Size : 46,8 Mb
Release : 2014-10-13
Category : Mathematics
ISBN : 9783319114453

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Formal Algorithmic Elimination for PDEs by Daniel Robertz Pdf

Investigating the correspondence between systems of partial differential equations and their analytic solutions using a formal approach, this monograph presents algorithms to determine the set of analytic solutions of such a system and conversely to find differential equations whose set of solutions coincides with a given parametrized set of analytic functions. After giving a detailed introduction to Janet bases and Thomas decomposition, the problem of finding an implicit description of certain sets of analytic functions in terms of differential equations is addressed. Effective methods of varying generality are developed to solve the differential elimination problems that arise in this context. In particular, it is demonstrated how the symbolic solution of partial differential equations profits from the study of the implicitization problem. For instance, certain families of exact solutions of the Navier-Stokes equations can be computed.

Computer Algebra in Scientific Computing

Matthew England,Wolfram Koepf,Timur M. Sadykov,Werner M. Seiler,Evgenii V. Vorozhtsov
Computer Algebra in Scientific Computing Book PDF

Author : Matthew England,Wolfram Koepf,Timur M. Sadykov,Werner M. Seiler,Evgenii V. Vorozhtsov
Publisher : Springer
Page : 479 pages
File Size : 51,8 Mb
Release : 2019-08-15
Category : Computers
ISBN : 9783030268312

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Computer Algebra in Scientific Computing by Matthew England,Wolfram Koepf,Timur M. Sadykov,Werner M. Seiler,Evgenii V. Vorozhtsov Pdf

This book constitutes the refereed proceedings of the 21st International Workshop on Computer Algebra in Scientific Computing, CASC 2019, held in Moscow, Russia, in August 2019. The 28 full papers presented together with 2 invited talks were carefully reviewed and selected from 44 submissions. They deal with cutting-edge research in all major disciplines of computer algebra. The papers cover topics such as polynomial algebra, symbolic and symbolic-numerical computation, applications of symbolic computation for investigating and solving ordinary differential equations, applications of CASs in the investigation and solution of celestial mechanics problems, and in mechanics, physics, and robotics.

Algebraic and Symbolic Computation Methods in Dynamical Systems

Alban Quadrat,Eva Zerz
Algebraic and Symbolic Computation Methods in Dynamical Systems Book PDF

Author : Alban Quadrat,Eva Zerz
Publisher : Springer Nature
Page : 320 pages
File Size : 47,5 Mb
Release : 2020-05-30
Category : Science
ISBN : 9783030383565

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Algebraic and Symbolic Computation Methods in Dynamical Systems by Alban Quadrat,Eva Zerz Pdf

This book aims at reviewing recent progress in the direction of algebraic and symbolic computation methods for functional systems, e.g. ODE systems, differential time-delay equations, difference equations and integro-differential equations. In the nineties, modern algebraic theories were introduced in mathematical systems theory and in control theory. Combined with real algebraic geometry, which was previously introduced in control theory, the past years have seen a flourishing development of algebraic methods in control theory. One of the strengths of algebraic methods lies in their close connections to computations. The use of the above-mentioned algebraic theories in control theory has been an important source of motivation to develop effective versions of these theories (when possible). With the development of computer algebra and computer algebra systems, symbolic methods for control theory have been developed over the past years. The goal of this book is to propose a partial state of the art in this direction. To make recent results more easily accessible to a large audience, the chapters include materials which survey the main mathematical methods and results and which are illustrated with explicit examples.

Computer Algebra in Scientific Computing

Vladimir P. Gerdt,Wolfram Koepf,Werner M. Seiler,Evgenii V. Vorozhtsov
Computer Algebra in Scientific Computing Book PDF

Author : Vladimir P. Gerdt,Wolfram Koepf,Werner M. Seiler,Evgenii V. Vorozhtsov
Publisher : Springer
Page : 494 pages
File Size : 48,9 Mb
Release : 2015-09-10
Category : Computers
ISBN : 9783319240213

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Computer Algebra in Scientific Computing by Vladimir P. Gerdt,Wolfram Koepf,Werner M. Seiler,Evgenii V. Vorozhtsov Pdf

This book constitutes the proceedings of the 17th International Workshop on Computer Algebra in Scientific Computing, CASC 2015, held in Aachen, Germany, in September 2015. The 35 full papers presented in this volume were carefully reviewed and selected from 42 submissions. They deal with the ongoing progress both in theoretical computer algebra and its expanding applications. New and closer interactions are fostered by combining the area of computer algebra methods and systems and the application of the tools of computer algebra for the solution of problems in scientific computing.

Computer Algebra in Scientific Computing

François Boulier,Matthew England,Timur M. Sadykov,Evgenii V. Vorozhtsov
Computer Algebra in Scientific Computing Book PDF

Author : François Boulier,Matthew England,Timur M. Sadykov,Evgenii V. Vorozhtsov
Publisher : Springer Nature
Page : 644 pages
File Size : 46,8 Mb
Release : 2020-10-17
Category : Computers
ISBN : 9783030600266

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Computer Algebra in Scientific Computing by François Boulier,Matthew England,Timur M. Sadykov,Evgenii V. Vorozhtsov Pdf

This book constitutes the refereed proceedings of the 22nd International Workshop on Computer Algebra in Scientific Computing, CASC 2020, held in Linz, Austria, in September 2020. The conference was held virtually due to the COVID-19 pandemic. The 34 full papers presented together with 2 invited talks were carefully reviewed and selected from 41 submissions. They deal with cutting-edge research in all major disciplines of computer algebra. The papers cover topics such as polynomial algebra, symbolic and symbolic-numerical computation, applications of symbolic computation for investigating and solving ordinary differential equations, applications of CAS in the investigation and solution of celestial mechanics problems, and in mechanics, physics, and robotics.

Quantitative Evaluation of Systems

Marco Gribaudo,David N. Jansen,Anne Remke
Quantitative Evaluation of Systems Book PDF

Author : Marco Gribaudo,David N. Jansen,Anne Remke
Publisher : Springer Nature
Page : 301 pages
File Size : 41,9 Mb
Release : 2020-11-03
Category : Computers
ISBN : 9783030598549

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Quantitative Evaluation of Systems by Marco Gribaudo,David N. Jansen,Anne Remke Pdf

This book constitutes the proceedings of the 17th International Conference on Quantitative Evaluation Systems, QEST 2020, held in Vienna, Austria, in August/September 2020. The 12 full papers presented together with 7 short papers were carefully reviewed and selected from 42 submissions. The papers cover topics such as classic measures involving performance and reliability, quantification of properties that are classically qualitative, such as safety, correctness, and security as well as analytic studies, diversity in the model formalisms and methodologies employed, and development of new formalisms and methodologies.

Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers

Kenji Iohara,Philippe Malbos,Masa-Hiko Saito,Nobuki Takayama
Two Algebraic Byways from Differential Equations Gr bner Bases and Quivers Book PDF

Author : Kenji Iohara,Philippe Malbos,Masa-Hiko Saito,Nobuki Takayama
Publisher : Springer Nature
Page : 375 pages
File Size : 49,9 Mb
Release : 2020-02-20
Category : Mathematics
ISBN : 9783030264543

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Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers by Kenji Iohara,Philippe Malbos,Masa-Hiko Saito,Nobuki Takayama Pdf

This edited volume presents a fascinating collection of lecture notes focusing on differential equations from two viewpoints: formal calculus (through the theory of Gröbner bases) and geometry (via quiver theory). Gröbner bases serve as effective models for computation in algebras of various types. Although the theory of Gröbner bases was developed in the second half of the 20th century, many works on computational methods in algebra were published well before the introduction of the modern algebraic language. Since then, new algorithms have been developed and the theory itself has greatly expanded. In comparison, diagrammatic methods in representation theory are relatively new, with the quiver varieties only being introduced – with big impact – in the 1990s. Divided into two parts, the book first discusses the theory of Gröbner bases in their commutative and noncommutative contexts, with a focus on algorithmic aspects and applications of Gröbner bases to analysis on systems of partial differential equations, effective analysis on rings of differential operators, and homological algebra. It then introduces representations of quivers, quiver varieties and their applications to the moduli spaces of meromorphic connections on the complex projective line. While no particular reader background is assumed, the book is intended for graduate students in mathematics, engineering and related fields, as well as researchers and scholars.

Elimination Methods

D. Wang
Elimination Methods Book PDF

Author : D. Wang
Publisher : Springer Science & Business Media
Page : 268 pages
File Size : 49,9 Mb
Release : 2001-01-05
Category : Computers
ISBN : 3211832416

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Elimination Methods by D. Wang Pdf

This book provides a systematic and uniform presentation of elimination methods and the underlying theories, along the central line of decomposing arbitrary systems of polynomials into triangular systems of various kinds. Highlighting methods based on triangular sets, the book also covers the theory and techniques of resultants and Gröbner bases. The methods and their efficiency are illustrated by fully worked out examples and their applications to selected problems such as from polynomial ideal theory, automated theorem proving in geometry and the qualitative study of differential equations. The reader will find the formally described algorithms ready for immediate implementation and applicable to many other problems. Suitable as a graduate text, this book offers an indispensable reference for everyone interested in mathematical computation, computer algebra (software), and systems of algebraic equations.

Adaptive Numerical Solution of PDEs

Peter Deuflhard,Martin Weiser
Adaptive Numerical Solution of PDEs Book PDF

Author : Peter Deuflhard,Martin Weiser
Publisher : Walter de Gruyter
Page : 436 pages
File Size : 42,7 Mb
Release : 2012-08-31
Category : Mathematics
ISBN : 9783110283112

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Adaptive Numerical Solution of PDEs by Peter Deuflhard,Martin Weiser Pdf

This book deals with the general topic “Numerical solution of partial differential equations (PDEs)” with a focus on adaptivity of discretizations in space and time. By and large, introductory textbooks like “Numerical Analysis in Modern Scientific Computing” by Deuflhard and Hohmann should suffice as a prerequisite. The emphasis lies on elliptic and parabolic systems. Hyperbolic conservation laws are treated only on an elementary level excluding turbulence. Numerical Analysis is clearly understood as part of Scientific Computing. The focus is on the efficiency of algorithms, i.e. speed, reliability, and robustness, which directly leads to the concept of adaptivity in algorithms. The theoretical derivation and analysis is kept as elementary as possible. Nevertheless required somewhat more sophisticated mathematical theory is summarized in comprehensive form in an appendix. Complex relations are explained by numerous figures and illustrating examples. Non-trivial problems from regenerative energy, nanotechnology, surgery, and physiology are inserted. The text will appeal to graduate students and researchers on the job in mathematics, science, and technology. Conceptually, it has been written as a textbook including exercises and a software list, but at the same time it should be well-suited for self-study.

The Theory of Difference Schemes

Alexander A. Samarskii
The Theory of Difference Schemes Book PDF

Author : Alexander A. Samarskii
Publisher : CRC Press
Page : 796 pages
File Size : 50,7 Mb
Release : 2001-03-29
Category : Mathematics
ISBN : 0203908511

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The Theory of Difference Schemes by Alexander A. Samarskii Pdf

The Theory of Difference Schemes emphasizes solutions to boundary value problems through multiple difference schemes. It addresses the construction of approximate numerical methods and computer algorithms for solving mathematical physics problems. The book also develops mathematical models for obtaining desired solutions in minimal time using direct or iterative difference equations. Mathematical Reviews said it is "well-written [and] an excellent book, with a wealth of mathematical material and techniques."

University of Michigan Official Publication

University of Michigan
University of Michigan Official Publication Book PDF

Author : University of Michigan
Publisher : UM Libraries
Page : 760 pages
File Size : 51,7 Mb
Release : 1972
Category : Education, Higher
ISBN : UOM:39015078739284

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University of Michigan Official Publication by University of Michigan Pdf

Each number is the catalogue of a specific school or college of the University.

Numerical Algorithms

Justin Solomon
Numerical Algorithms Book PDF

Author : Justin Solomon
Publisher : CRC Press
Page : 400 pages
File Size : 44,7 Mb
Release : 2015-06-24
Category : Computers
ISBN : 9781482251890

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Numerical Algorithms by Justin Solomon Pdf

Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic desig

Computational Partial Differential Equations

Hans Petter Langtangen
Computational Partial Differential Equations Book PDF

Author : Hans Petter Langtangen
Publisher : Springer Science & Business Media
Page : 704 pages
File Size : 51,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662011706

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Computational Partial Differential Equations by Hans Petter Langtangen Pdf

Targeted at students and researchers in computational sciences who need to develop computer codes for solving PDEs, the exposition here is focused on numerics and software related to mathematical models in solid and fluid mechanics. The book teaches finite element methods, and basic finite difference methods from a computational point of view, with the main emphasis on developing flexible computer programs, using the numerical library Diffpack. Diffpack is explained in detail for problems including model equations in applied mathematics, heat transfer, elasticity, and viscous fluid flow. All the program examples, as well as Diffpack for use with this book, are available on the Internet. XXXXXXX NEUER TEXT This book is for researchers who need to develop computer code for solving PDEs. Numerical methods and the application of Diffpack are explained in detail. Diffpack is a modern C++ development environment that is widely used by industrial scientists and engineers working in areas such as oil exploration, groundwater modeling, and materials testing. All the program examples, as well as a test version of Diffpack, are available for free over the Internet.

Solving PDEs in Python

Hans Petter Langtangen,Anders Logg
Solving PDEs in Python Book PDF

Author : Hans Petter Langtangen,Anders Logg
Publisher : Springer
Page : 152 pages
File Size : 51,7 Mb
Release : 2017-03-21
Category : Computers
ISBN : 9783319524627

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Solving PDEs in Python by Hans Petter Langtangen,Anders Logg Pdf

This book offers a concise and gentle introduction to finite element programming in Python based on the popular FEniCS software library. Using a series of examples, including the Poisson equation, the equations of linear elasticity, the incompressible Navier–Stokes equations, and systems of nonlinear advection–diffusion–reaction equations, it guides readers through the essential steps to quickly solving a PDE in FEniCS, such as how to define a finite variational problem, how to set boundary conditions, how to solve linear and nonlinear systems, and how to visualize solutions and structure finite element Python programs. This book is open access under a CC BY license.

Symbolic and Numerical Scientific Computation

Franz Winkler,Ulrich Langer
Symbolic and Numerical Scientific Computation Book PDF

Author : Franz Winkler,Ulrich Langer
Publisher : Springer
Page : 392 pages
File Size : 40,7 Mb
Release : 2003-08-03
Category : Computers
ISBN : 9783540450849

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Symbolic and Numerical Scientific Computation by Franz Winkler,Ulrich Langer Pdf

The thoroughly refereed post-proceedings of the Second International Conference on Symbolic and Numerical Scientific Computation, SNSC 2001, held in Hagenberg, Austria, in September 2001. The 19 revised full papers presented were carefully selected during two rounds of reviewing and improvement. The papers are organized in topical sections on symbolics and numerics of differential equations, symbolics and numerics in algebra and geometry, and applications in physics and engineering.