Introduction to Numerical Ordinary and Partial Differential Equations Using MATLAB PDF Download

Author: Alexander Stanoyevitch
Publisher: John Wiley & Sons
ISBN: 1118031504
Category : Mathematics
Languages : en
Pages : 834

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Book Description

Author: Jeffery M. Cooper
Publisher: Springer Science & Business Media
ISBN: 1461217547
Category : Mathematics
Languages : en
Pages : 549

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Book Description
Overview The subject of partial differential equations has an unchanging core of material but is constantly expanding and evolving. The core consists of solution methods, mainly separation of variables, for boundary value problems with constant coeffi cients in geometrically simple domains. Too often an introductory course focuses exclusively on these core problems and techniques and leaves the student with the impression that there is no more to the subject. Questions of existence, uniqueness, and well-posedness are ignored. In particular there is a lack of connection between the analytical side of the subject and the numerical side. Furthermore nonlinear problems are omitted because they are too hard to deal with analytically. Now, however, the availability of convenient, powerful computational software has made it possible to enlarge the scope of the introductory course. My goal in this text is to give the student a broader picture of the subject. In addition to the basic core subjects, I have included material on nonlinear problems and brief discussions of numerical methods. I feel that it is important for the student to see nonlinear problems and numerical methods at the beginning of the course, and not at the end when we run usually run out of time. Furthermore, numerical methods should be introduced for each equation as it is studied, not lumped together in a final chapter.

Author: Jichun Li
Publisher: CRC Press
ISBN: 0429556535
Category : Mathematics
Languages : en
Pages : 423

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Book Description
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
ISBN: 9814635111
Category : Mathematics
Languages : en
Pages : 346

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Book Description
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: Martin J. Gander
Publisher: SIAM
ISBN: 1611975301
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: Matthew P. Coleman
Publisher: CRC Press
ISBN: 9781032650869
Category : Mathematics
Languages : en
Pages : 0

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Book Description
"The first and second editions of "An Introduction to Partial Differential Equation with MATLAB®" gained popularity among instructors and students at various universities throughout the world. Plain mathematical language is used in a friendly manner to provide a basic introduction to partial differential equations focusing on Fourier series and integrals. Suitable for a one- or two-semester introduction to PDEs and Fourier series, the book offers equations based on method of solution and provides both physical and mathematical motivation as much as possible. This third edition changes the book structure by lifting the role of the computational part much closer to the revised analytical portion. The re-designed content will be extremely useful for students of mathematics, physics and engineering who would like to focus on the practical aspects of using the theory of PDEs for modeling and later while taking various courses in numerical analysis, computer science, PDE-based programming, and optimization. Included in this new edition is a substantial amount of material on reviewing computational methods for solving ODEs (symbolically and numerically), visualizing solutions of PDEs, using MATLAB's symbolic programming toolbox, and applying various numerical schemes for computing with regard to numerical solutions in practical applications, along with suggestions for topics of course projects. Students will use sample MATLAB and Python codes available online for their practical experiments and for completing computational lab assignments and course projects"--

Author: Alain Vande Wouwer
Publisher: Springer
ISBN: 3319067907
Category : Technology & Engineering
Languages : en
Pages : 416

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Book Description
Simulation of ODE/PDE Models with MATLAB®, OCTAVE and SCILAB shows the reader how to exploit a fuller array of numerical methods for the analysis of complex scientific and engineering systems than is conventionally employed. The book is dedicated to numerical simulation of distributed parameter systems described by mixed systems of algebraic equations, ordinary differential equations (ODEs) and partial differential equations (PDEs). Special attention is paid to the numerical method of lines (MOL), a popular approach to the solution of time-dependent PDEs, which proceeds in two basic steps: spatial discretization and time integration. Besides conventional finite-difference and element techniques, more advanced spatial-approximation methods are examined in some detail, including nonoscillatory schemes and adaptive-grid approaches. A MOL toolbox has been developed within MATLAB®/OCTAVE/SCILAB. In addition to a set of spatial approximations and time integrators, this toolbox includes a collection of application examples, in specific areas, which can serve as templates for developing new programs. Simulation of ODE/PDE Models with MATLAB®, OCTAVE and SCILAB provides a practical introduction to some advanced computational techniques for dynamic system simulation, supported by many worked examples in the text, and a collection of codes available for download from the book’s page at www.springer.com. This text is suitable for self-study by practicing scientists and engineers and as a final-year undergraduate course or at the graduate level.

Author: Abdelwahab Kharab
Publisher: CRC Press
ISBN: 1351605917
Category : Mathematics
Languages : en
Pages : 447

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Book Description
Previous editions of this popular textbook offered an accessible and practical introduction to numerical analysis. An Introduction to Numerical Methods: A MATLAB® Approach, Fourth Edition continues to present a wide range of useful and important algorithms for scientific and engineering applications. The authors use MATLAB to illustrate each numerical method, providing full details of the computed results so that the main steps are easily visualized and interpreted. This edition also includes a new chapter on Dynamical Systems and Chaos. Features Covers the most common numerical methods encountered in science and engineering Illustrates the methods using MATLAB Presents numerous examples and exercises, with selected answers at the back of the book

Author: William Bober
Publisher: CRC Press
ISBN: 146657609X
Category : Mathematics
Languages : en
Pages : 544

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Book Description
Introduction to Numerical and Analytical Methods with MATLAB for Engineers and Scientists provides the basic concepts of programming in MATLAB for engineering applications. Teaches engineering students how to write computer programs on the MATLAB platform Examines the selection and use of numerical and analytical methods through examples and cas

Author: William Bober
Publisher: CRC Press
ISBN: 1466576022
Category : Mathematics
Languages : en
Pages : 558

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Book Description
Introduction to Numerical and Analytical Methods with MATLAB® for Engineers and Scientists provides the basic concepts of programming in MATLAB for engineering applications. • Teaches engineering students how to write computer programs on the MATLAB platform • Examines the selection and use of numerical and analytical methods through examples and case studies • Demonstrates mathematical concepts that can be used to help solve engineering problems, including matrices, roots of equations, integration, ordinary differential equations, curve fitting, algebraic linear equations, and more The text covers useful numerical methods, including interpolation, Simpson’s rule on integration, the Gauss elimination method for solving systems of linear algebraic equations, the Runge-Kutta method for solving ordinary differential equations, and the search method in combination with the bisection method for obtaining the roots of transcendental and polynomial equations. It also highlights MATLAB’s built-in functions. These include interp1 function, the quad and dblquad functions, the inv function, the ode45 function, the fzero function, and many others. The second half of the text covers more advanced topics, including the iteration method for solving pipe flow problems, the Hardy-Cross method for solving flow rates in a pipe network, separation of variables for solving partial differential equations, and the use of Laplace transforms to solve both ordinary and partial differential equations. This book serves as a textbook for a first course in numerical methods using MATLAB to solve problems in mechanical, civil, aeronautical, and electrical engineering. It can also be used as a textbook or as a reference book in higher level courses.