Author: Martin J. Gander
Publisher: SIAM
ISBN: 161197531X
Category : Science
Languages : en
Pages : 163
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Book Description
This book provides an elementary yet comprehensive introduction to the numerical solution of partial differential equations (PDEs). Used to model important phenomena, such as the heating of apartments and the behavior of electromagnetic waves, these equations have applications in engineering and the life sciences, and most can only be solved approximately using computers.? Numerical Analysis of Partial Differential Equations Using Maple and MATLAB provides detailed descriptions of the four major classes of discretization methods for PDEs (finite difference method, finite volume method, spectral method, and finite element method) and runnable MATLAB? code for each of the discretization methods and exercises. It also gives self-contained convergence proofs for each method using the tools and techniques required for the general convergence analysis but adapted to the simplest setting to keep the presentation clear and complete. This book is intended for advanced undergraduate and early graduate students in numerical analysis and scientific computing and researchers in related fields. It is appropriate for a course on numerical methods for partial differential equations.
Author: Graham Griffiths
Publisher: Academic Press
ISBN: 0123846536
Category : Mathematics
Languages : en
Pages : 463
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Book Description
Although the Partial Differential Equations (PDE) models that are now studied are usually beyond traditional mathematical analysis, the numerical methods that are being developed and used require testing and validation. This is often done with PDEs that have known, exact, analytical solutions. The development of analytical solutions is also an active area of research, with many advances being reported recently, particularly traveling wave solutions for nonlinear evolutionary PDEs. Thus, the current development of analytical solutions directly supports the development of numerical methods by providing a spectrum of test problems that can be used to evaluate numerical methods. This book surveys some of these new developments in analytical and numerical methods, and relates the two through a series of PDE examples. The PDEs that have been selected are largely "named'' since they carry the names of their original contributors. These names usually signify that the PDEs are widely recognized and used in many application areas. The authors' intention is to provide a set of numerical and analytical methods based on the concept of a traveling wave, with a central feature of conversion of the PDEs to ODEs. The Matlab and Maple software will be available for download from this website shortly. www.pdecomp.net - Includes a spectrum of applications in science, engineering, applied mathematics - Presents a combination of numerical and analytical methods - Provides transportable computer codes in Matlab and Maple
Author: H.J. Lee
Publisher: CRC Press
ISBN: 0203010515
Category : Mathematics
Languages : en
Pages : 528
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Book Description
This book provides a set of ODE/PDE integration routines in the six most widely used computer languages, enabling scientists and engineers to apply ODE/PDE analysis toward solving complex problems. This text concisely reviews integration algorithms, then analyzes the widely used Runge-Kutta method. It first presents a complete code before discussin
Author: Inna Shingareva
Publisher: Springer Science & Business Media
ISBN: 370910517X
Category : Mathematics
Languages : en
Pages : 372
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Book Description
The emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple and Mathematica, facilitates a deeper understanding of the subject. Among a big number of CAS, we choose the two systems, Maple and Mathematica, that are used worldwide by students, research mathematicians, scientists, and engineers. As in the our previous books, we propose the idea to use in parallel both systems, Maple and Mathematica, since in many research problems frequently it is required to compare independent results obtained by using different computer algebra systems, Maple and/or Mathematica, at all stages of the solution process. One of the main points (related to CAS) is based on the implementation of a whole solution method (e.g. starting from an analytical derivation of exact governing equations, constructing discretizations and analytical formulas of a numerical method, performing numerical procedure, obtaining various visualizations, and comparing the numerical solution obtained with other types of solutions considered in the book, e.g. with asymptotic solution).
Author: Mark S. Gockenbach
Publisher: SIAM
ISBN: 0898719356
Category : Mathematics
Languages : en
Pages : 665
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Book Description
A fresh, forward-looking undergraduate textbook that treats the finite element method and classical Fourier series method with equal emphasis.
Author: Zhilin Li
Publisher: World Scientific
ISBN: 9811228647
Category : Mathematics
Languages : en
Pages : 218
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Book Description
The book is designed for undergraduate or beginning level graduate students, and students from interdisciplinary areas including engineers, and others who need to use partial differential equations, Fourier series, Fourier and Laplace transforms. The prerequisite is a basic knowledge of calculus, linear algebra, and ordinary differential equations.The textbook aims to be practical, elementary, and reasonably rigorous; the book is concise in that it describes fundamental solution techniques for first order, second order, linear partial differential equations for general solutions, fundamental solutions, solution to Cauchy (initial value) problems, and boundary value problems for different PDEs in one and two dimensions, and different coordinates systems. Analytic solutions to boundary value problems are based on Sturm-Liouville eigenvalue problems and series solutions.The book is accompanied with enough well tested Maple files and some Matlab codes that are available online. The use of Maple makes the complicated series solution simple, interactive, and visible. These features distinguish the book from other textbooks available in the related area.
Author: Ioannis P. Stavroulakis
Publisher: World Scientific
ISBN: 9789812388155
Category : Mathematics
Languages : en
Pages : 328
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Book Description
This textbook is a self-contained introduction to partial differential equations.It has been designed for undergraduates and first year graduate students majoring in mathematics, physics, engineering, or science.The text provides an introduction to the basic equations of mathematical physics and the properties of their solutions, based on classical calculus and ordinary differential equations. Advanced concepts such as weak solutions and discontinuous solutions of nonlinear conservation laws are also considered.
Author: Zhilin Li
Publisher: Cambridge University Press
ISBN: 1107163226
Category : Mathematics
Languages : en
Pages : 305
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Book Description
A practical and concise guide to finite difference and finite element methods. Well-tested MATLAB® codes are available online.
Author: Lawrence F. Shampine
Publisher: Cambridge University Press
ISBN: 9780521530941
Category : Computers
Languages : en
Pages : 276
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Book Description
This concise text, first published in 2003, is for a one-semester course for upper-level undergraduates and beginning graduate students in engineering, science, and mathematics, and can also serve as a quick reference for professionals. The major topics in ordinary differential equations, initial value problems, boundary value problems, and delay differential equations, are usually taught in three separate semester-long courses. This single book provides a sound treatment of all three in fewer than 300 pages. Each chapter begins with a discussion of the 'facts of life' for the problem, mainly by means of examples. Numerical methods for the problem are then developed, but only those methods most widely used. The treatment of each method is brief and technical issues are minimized, but all the issues important in practice and for understanding the codes are discussed. The last part of each chapter is a tutorial that shows how to solve problems by means of small, but realistic, examples.
Author: G. Evans
Publisher: Springer Science & Business Media
ISBN: 1447103777
Category : Mathematics
Languages : en
Pages : 299
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Book Description
The subject of partial differential equations holds an exciting and special position in mathematics. Partial differential equations were not consciously created as a subject but emerged in the 18th century as ordinary differential equations failed to describe the physical principles being studied. The subject was originally developed by the major names of mathematics, in particular, Leonard Euler and Joseph-Louis Lagrange who studied waves on strings; Daniel Bernoulli and Euler who considered potential theory, with later developments by Adrien-Marie Legendre and Pierre-Simon Laplace; and Joseph Fourier's famous work on series expansions for the heat equation. Many of the greatest advances in modern science have been based on discovering the underlying partial differential equation for the process in question. James Clerk Maxwell, for example, put electricity and magnetism into a unified theory by establishing Maxwell's equations for electromagnetic theory, which gave solutions for prob lems in radio wave propagation, the diffraction of light and X-ray developments. Schrodinger's equation for quantum mechanical processes at the atomic level leads to experimentally verifiable results which have changed the face of atomic physics and chemistry in the 20th century. In fluid mechanics, the Navier Stokes' equations form a basis for huge number-crunching activities associated with such widely disparate topics as weather forecasting and the design of supersonic aircraft. Inevitably the study of partial differential equations is a large undertaking, and falls into several areas of mathematics.
