Numerical Solution Of Ordinary And Partial Differential Equations The 3rd Edition
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Numerical Solution Of Ordinary And Partial Differential Equations The 3rd Edition
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Author : Granville Sewell
language : en
Publisher: World Scientific
Release Date : 2014-12-16
Numerical Solution Of Ordinary And Partial Differential Equations The 3rd Edition written by Granville Sewell and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-16 with Mathematics categories.
This book presents methods for the computational solution of differential equations, both ordinary and partial, time-dependent and steady-state. Finite difference methods are introduced and analyzed in the first four chapters, and finite element methods are studied in chapter five. A very general-purpose and widely-used finite element program, PDE2D, which implements many of the methods studied in the earlier chapters, is presented and documented in Appendix A.The book contains the relevant theory and error analysis for most of the methods studied, but also emphasizes the practical aspects involved in implementing the methods. Students using this book will actually see and write programs (FORTRAN or MATLAB) for solving ordinary and partial differential equations, using both finite differences and finite elements. In addition, they will be able to solve very difficult partial differential equations using the software PDE2D, presented in Appendix A. PDE2D solves very general steady-state, time-dependent and eigenvalue PDE systems, in 1D intervals, general 2D regions, and a wide range of simple 3D regions.The Windows version of PDE2D comes free with every purchase of this book. More information at www.pde2d.com/contact.
Basic Partial Differential Equations
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Author : David. Bleecker
language : en
Publisher: CRC Press
Release Date : 2018-01-18
Basic Partial Differential Equations written by David. Bleecker and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-18 with Mathematics categories.
Methods of solution for partial differential equations (PDEs) used in mathematics, science, and engineering are clarified in this self-contained source. The reader will learn how to use PDEs to predict system behaviour from an initial state of the system and from external influences, and enhance the success of endeavours involving reasonably smooth, predictable changes of measurable quantities. This text enables the reader to not only find solutions of many PDEs, but also to interpret and use these solutions. It offers 6000 exercises ranging from routine to challenging. The palatable, motivated proofs enhance understanding and retention of the material. Topics not usually found in books at this level include but examined in this text: the application of linear and nonlinear first-order PDEs to the evolution of population densities and to traffic shocks convergence of numerical solutions of PDEs and implementation on a computer convergence of Laplace series on spheres quantum mechanics of the hydrogen atom solving PDEs on manifolds The text requires some knowledge of calculus but none on differential equations or linear algebra.
Numerical Analysis With Algorithms And Programming
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Author : Santanu Saha Ray
language : en
Publisher: CRC Press
Release Date : 2018-09-03
Numerical Analysis With Algorithms And Programming written by Santanu Saha Ray and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-03 with Mathematics categories.
Numerical Analysis with Algorithms and Programming is the first comprehensive textbook to provide detailed coverage of numerical methods, their algorithms, and corresponding computer programs. It presents many techniques for the efficient numerical solution of problems in science and engineering. Along with numerous worked-out examples, end-of-chapter exercises, and Mathematica® programs, the book includes the standard algorithms for numerical computation: Root finding for nonlinear equations Interpolation and approximation of functions by simpler computational building blocks, such as polynomials and splines The solution of systems of linear equations and triangularization Approximation of functions and least square approximation Numerical differentiation and divided differences Numerical quadrature and integration Numerical solutions of ordinary differential equations (ODEs) and boundary value problems Numerical solution of partial differential equations (PDEs) The text develops students’ understanding of the construction of numerical algorithms and the applicability of the methods. By thoroughly studying the algorithms, students will discover how various methods provide accuracy, efficiency, scalability, and stability for large-scale systems.
Ode Bvp And 1d Pde Solvers For Scientific And Engineering Problems With Matlab Basics
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Author : Burstein, Leonid
language : en
Publisher: IGI Global
Release Date : 2025-02-06
Ode Bvp And 1d Pde Solvers For Scientific And Engineering Problems With Matlab Basics written by Burstein, Leonid and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-06 with Computers categories.
In the academic field, engineers, scientists, educators, and students are faced with a persistent challenge: the gap between theoretical knowledge and practical implementation in solving real-world engineering problems. The scarcity of focused resources tailored to mastering MATLAB® and its specialized solvers for Ordinary Differential Equations (ODEs) and One-Dimensional Partial Differential Equations (1D PDEs) has left many individuals struggling to bridge this educational chasm. The disconnect between the theory learned in the classroom and the ability to effectively address engineering challenges in the real world has become a significant hurdle. The definitive solution to the academic conundrum of this lack of a focused resource is the book, ODE, BVP, and 1D PDE Solvers for Scientific and Engineering Problems with MATLAB Basics, which draws on years of teaching experience. This groundbreaking book provides a structured and holistic learning path designed to empower both novice learners and seasoned professionals. It takes readers on a comprehensive journey, commencing with the fundamentals of MATLAB® software and culminating in the mastery of its application in solving ODEs and 1D PDEs for a broad range of engineering problems.
Partial Differential Equations In Mechanics 1
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Author : A.P.S. Selvadurai
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-10-19
Partial Differential Equations In Mechanics 1 written by A.P.S. Selvadurai and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-10-19 with Mathematics categories.
This two-volume work focuses on partial differential equations (PDEs) with important applications in mechanical and civil engineering, emphasizing mathematical correctness, analysis, and verification of solutions. The presentation involves a discussion of relevant PDE applications, its derivation, and the formulation of consistent boundary conditions.
Differential Equations
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Author : Dr. Mahadev Biradar
language : en
Publisher: Shineeks Publishers
Release Date : 2024-10-15
Differential Equations written by Dr. Mahadev Biradar and has been published by Shineeks Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-15 with Education categories.
Differential Equations: Methods & Applications offers a comprehensive exploration of differential equations, essential tools for modeling dynamic systems in science and engineering. The book begins with foundational concepts and definitions, progressing through various techniques for solving first-order and second-order linear differential equations, including methods such as Laplace transforms and systems of differential equations. Numerical methods are also highlighted, alongside partial differential equations, emphasizing their applications in physics and engineering. The book concludes with discussions on advanced topics like boundary value problems and Sturm-Liouville theory. Designed for students and professionals, this text combines theory and practical applications, equipping readers with the necessary skills to tackle real-world problems involving differential equations.
Matrix Methods Of Structural Analysis
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Author : M. B. Kanchi
language : en
Publisher: New Age International
Release Date : 1993
Matrix Methods Of Structural Analysis written by M. B. Kanchi and has been published by New Age International this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
Finite Element Analysis Of Acoustic Scattering
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Author : Frank Ihlenburg
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-29
Finite Element Analysis Of Acoustic Scattering written by Frank Ihlenburg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-29 with Mathematics categories.
A cognitive journey towards the reliable simulation of scattering problems using finite element methods, with the pre-asymptotic analysis of Galerkin FEM for the Helmholtz equation with moderate and large wave number forming the core of this book. Starting from the basic physical assumptions, the author methodically develops both the strong and weak forms of the governing equations, while the main chapter on finite element analysis is preceded by a systematic treatment of Galerkin methods for indefinite sesquilinear forms. In the final chapter, three dimensional computational simulations are presented and compared with experimental data. The author also includes broad reference material on numerical methods for the Helmholtz equation in unbounded domains, including Dirichlet-to-Neumann methods, absorbing boundary conditions, infinite elements and the perfectly matched layer. A self-contained and easily readable work.
Configurational Forces As Basic Concepts Of Continuum Physics
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Author : Morton E. Gurtin
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-20
Configurational Forces As Basic Concepts Of Continuum Physics written by Morton E. Gurtin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-20 with Science categories.
For the last decade, the author has been working to extend continuum mechanics to treat moving boundaries in materials focusing, in particular, on problems of metallurgy. This monograph presents a rational treatment of the notion of configurational forces; it is an effort to promote a new viewpoint. Included is a presentation of configurational forces within a classical context and a discussion of their use in areas as diverse as phase transitions and fracture. The work should be of interest to materials scientists, mechanicians, and mathematicians.
Chaos Fractals And Noise
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Author : Andrzej Lasota
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Chaos Fractals And Noise written by Andrzej Lasota and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Mathematics categories.
The first edition of this book was originally published in 1985 under the ti tle "Probabilistic Properties of Deterministic Systems. " In the intervening years, interest in so-called "chaotic" systems has continued unabated but with a more thoughtful and sober eye toward applications, as befits a ma turing field. This interest in the serious usage of the concepts and techniques of nonlinear dynamics by applied scientists has probably been spurred more by the availability of inexpensive computers than by any other factor. Thus, computer experiments have been prominent, suggesting the wealth of phe nomena that may be resident in nonlinear systems. In particular, they allow one to observe the interdependence between the deterministic and probabilistic properties of these systems such as the existence of invariant measures and densities, statistical stability and periodicity, the influence of stochastic perturbations, the formation of attractors, and many others. The aim of the book, and especially of this second edition, is to present recent theoretical methods which allow one to study these effects. We have taken the opportunity in this second edition to not only correct the errors of the first edition, but also to add substantially new material in five sections and a new chapter.