Numerical Solutions Of Partial Differential Equations Using Finite Difference Method And Mathematica PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Numerical Solutions Of Partial Differential Equations Using Finite Difference Method And Mathematica PDF full book. Access full book title Numerical Solutions Of Partial Differential Equations Using Finite Difference Method And Mathematica.
| Author | : SUJAUL CHOWDHURY |
| Publisher | : American Academic Press |
| Total Pages | : 94 |
| Release | : 2019-01-14 |
| Genre | : Mathematics |
| ISBN | : 1631819933 |
Download NUMERICAL SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS USING FINITE DIFFERENCE METHOD AND MATHEMATICA Book in PDF, ePub and Kindle
The book is intended for graduate students of Engineering, Mathematics and Physics. We have numerically solved Hyperbolic and Parabolic partial differential equations with various initial conditions using Finite Difference Method and Mathematica. Replacing derivatives by finite difference approximations in these differential equations in conjunction with boundary conditions and initial conditions lead to equations relating numerical solutions at various position and time. These relations are intricate in that numerical value of the solution at one particular position and time is related with that at several other position and time. We have surmounted the intricacies by writing programs in Mathematica 6.0 that neatly provide systematic tabulation of the numerical values for all necessary position and time. This enabled us to plot the solutions as functions of position and time. Comparison with analytic solutions revealed nearly perfect match in every case. We have demonstrated conditions under which the nearly perfect match can be obtained even for larger increments in position or time.
| Author | : J.W. Thomas |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 451 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 1489972781 |
Download Numerical Partial Differential Equations: Finite Difference Methods Book in PDF, ePub and Kindle
What makes this book stand out from the competition is that it is more computational. Once done with both volumes, readers will have the tools to attack a wider variety of problems than those worked out in the competitors' books. The author stresses the use of technology throughout the text, allowing students to utilize it as much as possible.
| Author | : Victor Grigor'e Ganzha |
| Publisher | : CRC Press |
| Total Pages | : 347 |
| Release | : 2017-11-22 |
| Genre | : Mathematics |
| ISBN | : 1351427520 |
Download Numerical Solutions for Partial Differential Equations Book in PDF, ePub and Kindle
Partial differential equations (PDEs) play an important role in the natural sciences and technology, because they describe the way systems (natural and other) behave. The inherent suitability of PDEs to characterizing the nature, motion, and evolution of systems, has led to their wide-ranging use in numerical models that are developed in order to analyze systems that are not otherwise easily studied. Numerical Solutions for Partial Differential Equations contains all the details necessary for the reader to understand the principles and applications of advanced numerical methods for solving PDEs. In addition, it shows how the modern computer system algebra Mathematica® can be used for the analytic investigation of such numerical properties as stability, approximation, and dispersion.
| Author | : Randall J. LeVeque |
| Publisher | : SIAM |
| Total Pages | : 356 |
| Release | : 2007-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780898717839 |
Download Finite Difference Methods for Ordinary and Partial Differential Equations Book in PDF, ePub and Kindle
This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
| Author | : Martin J. Gander |
| Publisher | : SIAM |
| Total Pages | : 163 |
| Release | : 2018-01-01 |
| Genre | : Science |
| ISBN | : 1611975301 |
Download Numerical Analysis of Partial Differential Equations Using Maple and MATLAB Book in PDF, ePub and Kindle
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 | : Stig Larsson |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 263 |
| Release | : 2008-12-05 |
| Genre | : Mathematics |
| ISBN | : 3540887059 |
Download Partial Differential Equations with Numerical Methods Book in PDF, ePub and Kindle
The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.
| Author | : Boško S. Jovanović |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 416 |
| Release | : 2013-10-22 |
| Genre | : Mathematics |
| ISBN | : 1447154606 |
Download Analysis of Finite Difference Schemes Book in PDF, ePub and Kindle
This book develops a systematic and rigorous mathematical theory of finite difference methods for linear elliptic, parabolic and hyperbolic partial differential equations with nonsmooth solutions. Finite difference methods are a classical class of techniques for the numerical approximation of partial differential equations. Traditionally, their convergence analysis presupposes the smoothness of the coefficients, source terms, initial and boundary data, and of the associated solution to the differential equation. This then enables the application of elementary analytical tools to explore their stability and accuracy. The assumptions on the smoothness of the data and of the associated analytical solution are however frequently unrealistic. There is a wealth of boundary – and initial – value problems, arising from various applications in physics and engineering, where the data and the corresponding solution exhibit lack of regularity. In such instances classical techniques for the error analysis of finite difference schemes break down. The objective of this book is to develop the mathematical theory of finite difference schemes for linear partial differential equations with nonsmooth solutions. Analysis of Finite Difference Schemes is aimed at researchers and graduate students interested in the mathematical theory of numerical methods for the approximate solution of partial differential equations.
| Author | : Jichun Li |
| Publisher | : CRC Press |
| Total Pages | : 423 |
| Release | : 2019-09-26 |
| Genre | : Mathematics |
| ISBN | : 0429556535 |
Download Computational Partial Differential Equations Using MATLAB® Book in PDF, ePub and Kindle
In this popular text for an Numerical Analysis course, the authors introduce several major methods of solving various partial differential equations (PDEs) including elliptic, parabolic, and hyperbolic equations. It covers traditional techniques including the classic finite difference method, finite element method, and state-of-the-art numercial methods.The text uniquely emphasizes both theoretical numerical analysis and practical implementation of the algorithms in MATLAB. This new edition includes a new chapter, Finite Value Method, the presentation has been tightened, new exercises and applications are included, and the text refers now to the latest release of MATLAB. Key Selling Points: A successful textbook for an undergraduate text on numerical analysis or methods taught in mathematics and computer engineering. This course is taught in every university throughout the world with an engineering department or school. Competitive advantage broader numerical methods (including finite difference, finite element, meshless method, and finite volume method), provides the MATLAB source code for most popular PDEs with detailed explanation about the implementation and theoretical analysis. No other existing textbook in the market offers a good combination of theoretical depth and practical source codes.
| Author | : Granville Sewell |
| Publisher | : World Scientific |
| Total Pages | : 346 |
| Release | : 2014-12-16 |
| Genre | : Mathematics |
| ISBN | : 9814635111 |
Download Numerical Solution Of Ordinary And Partial Differential Equations, The (3rd Edition) Book in PDF, ePub and Kindle
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.
| Author | : Granville Sewell |
| Publisher | : Academic Press |
| Total Pages | : 284 |
| Release | : 2014-05-10 |
| Genre | : Mathematics |
| ISBN | : 1483259145 |
Download The Numerical Solution of Ordinary and Partial Differential Equations Book in PDF, ePub and Kindle
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.
