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Numerical Solution Of Ordinary And Partial Differential Equations, The (3rd Edition)

2014-12-16 Mathematics
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Release : 2014-12-16
Genre : Mathematics
Kind : eBook
Book Rating : 111/5 ( reviews)

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Book Synopsis Numerical Solution Of Ordinary And Partial Differential Equations, The (3rd Edition) by : Granville Sewell

Download or read book Numerical Solution Of Ordinary And Partial Differential Equations, The (3rd Edition) written by Granville Sewell. This book was released on 2014-12-16. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Numerical Solution of Ordinary and Partial Differential Equations

2014-05-10 Mathematics
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Release : 2014-05-10
Genre : Mathematics
Kind : eBook
Book Rating : 145/5 ( reviews)

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Book Synopsis The Numerical Solution of Ordinary and Partial Differential Equations by : Granville Sewell

Download or read book The Numerical Solution of Ordinary and Partial Differential Equations written by Granville Sewell. This book was released on 2014-05-10. Available in PDF, EPUB and Kindle. Book excerpt: The Numerical Solution of Ordinary and Partial Differential Equations is an introduction to the numerical solution of ordinary and partial differential equations. Finite difference methods for solving partial differential equations are mostly classical low order formulas, easy to program but not ideal for problems with poorly behaved solutions or (especially) for problems in irregular multidimensional regions. FORTRAN77 programs are used to implement many of the methods studied. Comprised of six chapters, this book begins with a review of direct methods for the solution of linear systems, with emphasis on the special features of the linear systems that arise when differential equations are solved. The next four chapters deal with the more commonly used finite difference methods for solving a variety of problems, including both ordinary differential equations and partial differential equations, and both initial value and boundary value problems. The final chapter is an overview of the basic ideas behind the finite element method and covers the Galerkin method for boundary value problems. Examples using piecewise linear trial functions, cubic hermite trial functions, and triangular elements are presented. This monograph is appropriate for senior-level undergraduate or first-year graduate students of mathematics.

Numerical Solution of Ordinary Differential Equations

2018-10-24 Mathematics
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Release : 2018-10-24
Genre : Mathematics
Kind : eBook
Book Rating : 555/5 ( reviews)

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Book Synopsis Numerical Solution of Ordinary Differential Equations by : L.F. Shampine

Download or read book Numerical Solution of Ordinary Differential Equations written by L.F. Shampine. This book was released on 2018-10-24. Available in PDF, EPUB and Kindle. Book excerpt: This new work is an introduction to the numerical solution of the initial value problem for a system of ordinary differential equations. The first three chapters are general in nature, and chapters 4 through 8 derive the basic numerical methods, prove their convergence, study their stability and consider how to implement them effectively. The book focuses on the most important methods in practice and develops them fully, uses examples throughout, and emphasizes practical problem-solving methods.

Applied Partial Differential Equations

2014-12-05 Mathematics
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Release : 2014-12-05
Genre : Mathematics
Kind : eBook
Book Rating : 935/5 ( reviews)

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Book Synopsis Applied Partial Differential Equations by : J. David Logan

Download or read book Applied Partial Differential Equations written by J. David Logan. This book was released on 2014-12-05. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is for the standard, one-semester, junior-senior course that often goes by the title "Elementary Partial Differential Equations" or "Boundary Value Problems". The audience consists of students in mathematics, engineering, and the sciences. The topics include derivations of some of the standard models of mathematical physics and methods for solving those equations on unbounded and bounded domains, and applications of PDE's to biology. The text differs from other texts in its brevity; yet it provides coverage of the main topics usually studied in the standard course, as well as an introduction to using computer algebra packages to solve and understand partial differential equations. For the 3rd edition the section on numerical methods has been considerably expanded to reflect their central role in PDE's. A treatment of the finite element method has been included and the code for numerical calculations is now written for MATLAB. Nonetheless the brevity of the text has been maintained. To further aid the reader in mastering the material and using the book, the clarity of the exercises has been improved, more routine exercises have been included, and the entire text has been visually reformatted to improve readability.

Analytic Methods for Partial Differential Equations

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 793/5 ( reviews)

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Book Synopsis Analytic Methods for Partial Differential Equations by : G. Evans

Download or read book Analytic Methods for Partial Differential Equations written by G. Evans. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: This is the practical introduction to the analytical approach taken in Volume 2. Based upon courses in partial differential equations over the last two decades, the text covers the classic canonical equations, with the method of separation of variables introduced at an early stage. The characteristic method for first order equations acts as an introduction to the classification of second order quasi-linear problems by characteristics. Attention then moves to different co-ordinate systems, primarily those with cylindrical or spherical symmetry. Hence a discussion of special functions arises quite naturally, and in each case the major properties are derived. The next section deals with the use of integral transforms and extensive methods for inverting them, and concludes with links to the use of Fourier series.

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