Solving Pdes In C

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Solving PDEs in C++

Yair Shapira
Solving PDEs in C Book PDF

Author : Yair Shapira
Publisher : SIAM
Page : 775 pages
File Size : 54,9 Mb
Release : 2012-06-07
Category : Computers
ISBN : 9781611972160

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Solving PDEs in C++ by Yair Shapira Pdf

In this much-expanded second edition, author Yair Shapira presents new applications and a substantial extension of the original object-oriented framework to make this popular and comprehensive book even easier to understand and use. It not only introduces the C and C++ programming languages, but also shows how to use them in the numerical solution of partial differential equations (PDEs). The book leads readers through the entire solution process, from the original PDE, through the discretization stage, to the numerical solution of the resulting algebraic system. The high level of abstraction available in C++ is particularly useful in the implementation of complex mathematical objects, such as unstructured mesh, sparse matrix, and multigrid hierarchy, often used in numerical modeling. The well-debugged and tested code segments implement the numerical methods efficiently and transparently in a unified object-oriented approach.

Ordinary and Partial Differential Equation Routines in C, C++, Fortran, Java, Maple, and MATLAB

H.J. Lee,W.E. Schiesser
Ordinary and Partial Differential Equation Routines in C C Fortran Java Maple and MATLAB Book PDF

Author : H.J. Lee,W.E. Schiesser
Publisher : CRC Press
Page : 528 pages
File Size : 55,6 Mb
Release : 2003-11-24
Category : Mathematics
ISBN : 9780203010518

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Ordinary and Partial Differential Equation Routines in C, C++, Fortran, Java, Maple, and MATLAB by H.J. Lee,W.E. Schiesser Pdf

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

Solving PDEs in C++

Yair Shapira
Solving PDEs in C Book PDF

Author : Yair Shapira
Publisher : Unknown
Page : 765 pages
File Size : 50,7 Mb
Release : 2012
Category : C++ (Computer program language)
ISBN : 1611972175

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Solving PDEs in C++ by Yair Shapira Pdf

In this much-expanded second edition, author Yair Shapira presents new applications and a substantial extension of the original object-oriented framework to make this popular and comprehensive book even easier to understand and use. It not only introduces the C and C++ programming languages, but also shows how to use them in the numerical solution of partial differential equations (PDEs). New material in this edition includes new chapters on 3-D nonlinear applications and image processing applications; new sections on cryptography applications; and even more new sections, many including additional algorithms. The book leads readers through the entire solution process, from the original PDE, through the discretization stage, to the numerical solution of the resulting algebraic system. The high level of abstraction available in C++ is particularly useful in the implementation of complex mathematical objects, such as unstructured mesh, sparse matrix, and multigrid hierarchy, often used in numerical modeling. The well-debugged and tested code segments implement the numerical methods efficiently and transparently in a unified object-oriented approach.

PETSc for Partial Differential Equations: Numerical Solutions in C and Python

Ed Bueler
PETSc for Partial Differential Equations Numerical Solutions in C and Python Book PDF

Author : Ed Bueler
Publisher : SIAM
Page : 407 pages
File Size : 51,5 Mb
Release : 2020-10-22
Category : Mathematics
ISBN : 9781611976311

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PETSc for Partial Differential Equations: Numerical Solutions in C and Python by Ed Bueler Pdf

The Portable, Extensible Toolkit for Scientific Computation (PETSc) is an open-source library of advanced data structures and methods for solving linear and nonlinear equations and for managing discretizations. This book uses these modern numerical tools to demonstrate how to solve nonlinear partial differential equations (PDEs) in parallel. It starts from key mathematical concepts, such as Krylov space methods, preconditioning, multigrid, and Newton’s method. In PETSc these components are composed at run time into fast solvers. Discretizations are introduced from the beginning, with an emphasis on finite difference and finite element methodologies. The example C programs of the first 12 chapters, listed on the inside front cover, solve (mostly) elliptic and parabolic PDE problems. Discretization leads to large, sparse, and generally nonlinear systems of algebraic equations. For such problems, mathematical solver concepts are explained and illustrated through the examples, with sufficient context to speed further development. PETSc for Partial Differential Equations addresses both discretizations and fast solvers for PDEs, emphasizing practice more than theory. Well-structured examples lead to run-time choices that result in high solver performance and parallel scalability. The last two chapters build on the reader’s understanding of fast solver concepts when applying the Firedrake Python finite element solver library. This textbook, the first to cover PETSc programming for nonlinear PDEs, provides an on-ramp for graduate students and researchers to a major area of high-performance computing for science and engineering. It is suitable as a supplement for courses in scientific computing or numerical methods for differential equations.

Solving PDEs in Python

Hans Petter Langtangen,Anders Logg
Solving PDEs in Python Book PDF

Author : Hans Petter Langtangen,Anders Logg
Publisher : Springer
Page : 152 pages
File Size : 44,8 Mb
Release : 2017-03-21
Category : Computers
ISBN : 9783319524627

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Solving PDEs in Python by Hans Petter Langtangen,Anders Logg Pdf

This book offers a concise and gentle introduction to finite element programming in Python based on the popular FEniCS software library. Using a series of examples, including the Poisson equation, the equations of linear elasticity, the incompressible Navier–Stokes equations, and systems of nonlinear advection–diffusion–reaction equations, it guides readers through the essential steps to quickly solving a PDE in FEniCS, such as how to define a finite variational problem, how to set boundary conditions, how to solve linear and nonlinear systems, and how to visualize solutions and structure finite element Python programs. This book is open access under a CC BY license.

Partial Differential Equations

Walter A. Strauss
Partial Differential Equations Book PDF

Author : Walter A. Strauss
Publisher : John Wiley & Sons
Page : 467 pages
File Size : 43,7 Mb
Release : 2007-12-21
Category : Mathematics
ISBN : 9780470054567

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Partial Differential Equations by Walter A. Strauss Pdf

Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

Introductory Differential Equations

Martha L. L. Abell,James P. Braselton
Introductory Differential Equations Book PDF

Author : Martha L. L. Abell,James P. Braselton
Publisher : Academic Press
Page : 744 pages
File Size : 49,5 Mb
Release : 2009-09-09
Category : Mathematics
ISBN : 9780080958453

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Introductory Differential Equations by Martha L. L. Abell,James P. Braselton Pdf

This text is for courses that are typically called (Introductory) Differential Equations, (Introductory) Partial Differential Equations, Applied Mathematics, Fourier Series and Boundary Value Problems. The text is appropriate for two semester courses: the first typically emphasizes ordinary differential equations and their applications while the second emphasizes special techniques (like Laplace transforms) and partial differential equations. The texts follows a "traditional" curriculum and takes the "traditional" (rather than "dynamical systems") approach. Introductory Differential Equations is a text that follows a traditional approach and is appropriate for a first course in ordinary differential equations (including Laplace transforms) and a second course in Fourier series and boundary value problems. Note that some schools might prefer to move the Laplace transform material to the second course, which is why we have placed the chapter on Laplace transforms in its location in the text. Ancillaries like Differential Equations with Mathematica and/or Differential Equations with Maple would be recommended and/or required ancillaries depending on the school, course, or instructor. *Technology Icons These icons highlight text that is intended to alert students that technology may be used intelligently to solve a problem, encouraging logical thinking and application * Think About It Icons and Examples Examples that end in a question encourage students to think critically about what to do next, whether it is to use technology or focus on a graph to determine an outcome *Differential Equations at Work These are projects requiring students to think critically by having students answer questions based on different conditions, thus engaging students

Numerical Solution of Partial Differential Equations by the Finite Element Method

Claes Johnson
Numerical Solution of Partial Differential Equations by the Finite Element Method Book PDF

Author : Claes Johnson
Publisher : Courier Corporation
Page : 290 pages
File Size : 53,5 Mb
Release : 2012-05-23
Category : Mathematics
ISBN : 9780486131597

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Numerical Solution of Partial Differential Equations by the Finite Element Method by Claes Johnson Pdf

An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. Suitable for advanced undergraduate and graduate courses, it outlines clear connections with applications and considers numerous examples from a variety of science- and engineering-related specialties.This text encompasses all varieties of the basic linear partial differential equations, including elliptic, parabolic and hyperbolic problems, as well as stationary and time-dependent problems. Additional topics include finite element methods for integral equations, an introduction to nonlinear problems, and considerations of unique developments of finite element techniques related to parabolic problems, including methods for automatic time step control. The relevant mathematics are expressed in non-technical terms whenever possible, in the interests of keeping the treatment accessible to a majority of students.

A Tutorial on Elliptic PDE Solvers and Their Parallelization

Craig C. Douglas,Gundolf Haase,Ulrich Langer
A Tutorial on Elliptic PDE Solvers and Their Parallelization Book PDF

Author : Craig C. Douglas,Gundolf Haase,Ulrich Langer
Publisher : SIAM
Page : 153 pages
File Size : 46,5 Mb
Release : 2003-01-01
Category : Technology & Engineering
ISBN : 0898718171

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A Tutorial on Elliptic PDE Solvers and Their Parallelization by Craig C. Douglas,Gundolf Haase,Ulrich Langer Pdf

This compact yet thorough tutorial is the perfect introduction to the basic concepts of solving partial differential equations (PDEs) using parallel numerical methods. In just eight short chapters, the authors provide readers with enough basic knowledge of PDEs, discretization methods, solution techniques, parallel computers, parallel programming, and the run-time behavior of parallel algorithms to allow them to understand, develop, and implement parallel PDE solvers. Examples throughout the book are intentionally kept simple so that the parallelization strategies are not dominated by technical details.

Finite Difference Computing with PDEs

Hans Petter Langtangen,Svein Linge
Finite Difference Computing with PDEs Book PDF

Author : Hans Petter Langtangen,Svein Linge
Publisher : Springer
Page : 522 pages
File Size : 50,9 Mb
Release : 2017-06-21
Category : Computers
ISBN : 9783319554563

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Finite Difference Computing with PDEs by Hans Petter Langtangen,Svein Linge Pdf

This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.

Solving Differential Equations in R

Karline Soetaert,Jeff Cash,Francesca Mazzia
Solving Differential Equations in R Book PDF

Author : Karline Soetaert,Jeff Cash,Francesca Mazzia
Publisher : Springer Science & Business Media
Page : 258 pages
File Size : 41,5 Mb
Release : 2012-06-06
Category : Computers
ISBN : 9783642280702

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Solving Differential Equations in R by Karline Soetaert,Jeff Cash,Francesca Mazzia Pdf

Mathematics plays an important role in many scientific and engineering disciplines. This book deals with the numerical solution of differential equations, a very important branch of mathematics. Our aim is to give a practical and theoretical account of how to solve a large variety of differential equations, comprising ordinary differential equations, initial value problems and boundary value problems, differential algebraic equations, partial differential equations and delay differential equations. The solution of differential equations using R is the main focus of this book. It is therefore intended for the practitioner, the student and the scientist, who wants to know how to use R for solving differential equations. However, it has been our goal that non-mathematicians should at least understand the basics of the methods, while obtaining entrance into the relevant literature that provides more mathematical background. Therefore, each chapter that deals with R examples is preceded by a chapter where the theory behind the numerical methods being used is introduced. In the sections that deal with the use of R for solving differential equations, we have taken examples from a variety of disciplines, including biology, chemistry, physics, pharmacokinetics. Many examples are well-known test examples, used frequently in the field of numerical analysis.

Programming for Computations - MATLAB/Octave

Svein Linge,Hans Petter Langtangen
Programming for Computations MATLAB Octave Book PDF

Author : Svein Linge,Hans Petter Langtangen
Publisher : Springer
Page : 228 pages
File Size : 51,5 Mb
Release : 2016-08-01
Category : Computers
ISBN : 9783319324524

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Programming for Computations - MATLAB/Octave by Svein Linge,Hans Petter Langtangen Pdf

This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows the students to write simple programs for solving common mathematical problems with numerical methods in engineering and science courses. The emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.

Computational Partial Differential Equations

Hans Petter Langtangen
Computational Partial Differential Equations Book PDF

Author : Hans Petter Langtangen
Publisher : Springer Science & Business Media
Page : 704 pages
File Size : 54,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662011706

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Computational Partial Differential Equations by Hans Petter Langtangen Pdf

Targeted at students and researchers in computational sciences who need to develop computer codes for solving PDEs, the exposition here is focused on numerics and software related to mathematical models in solid and fluid mechanics. The book teaches finite element methods, and basic finite difference methods from a computational point of view, with the main emphasis on developing flexible computer programs, using the numerical library Diffpack. Diffpack is explained in detail for problems including model equations in applied mathematics, heat transfer, elasticity, and viscous fluid flow. All the program examples, as well as Diffpack for use with this book, are available on the Internet. XXXXXXX NEUER TEXT This book is for researchers who need to develop computer code for solving PDEs. Numerical methods and the application of Diffpack are explained in detail. Diffpack is a modern C++ development environment that is widely used by industrial scientists and engineers working in areas such as oil exploration, groundwater modeling, and materials testing. All the program examples, as well as a test version of Diffpack, are available for free over the Internet.

Solving Partial Differential Equation Applications with PDE2D

Granville Sewell
Solving Partial Differential Equation Applications with PDE2D Book PDF

Author : Granville Sewell
Publisher : John Wiley & Sons
Page : 224 pages
File Size : 55,7 Mb
Release : 2018-10-09
Category : Mathematics
ISBN : 9781119507932

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Solving Partial Differential Equation Applications with PDE2D by Granville Sewell Pdf

Solve engineering and scientific partial differential equation applications using the PDE2D software developed by the author Solving Partial Differential Equation Applications with PDE2D derives and solves a range of ordinary and partial differential equation (PDE) applications. This book describes an easy-to-use, general purpose, and time-tested PDE solver developed by the author that can be applied to a wide variety of science and engineering problems. The equations studied include many time-dependent, steady-state and eigenvalue applications such as diffusion, heat conduction and convection, image processing, math finance, fluid flow, and elasticity and quantum mechanics, in one, two, and three space dimensions. The author begins with some simple "0D" problems that give the reader an opportunity to become familiar with PDE2D before proceeding to more difficult problems. The book ends with the solution of a very difficult nonlinear problem, which requires a moving adaptive grid because the solution has sharp, moving peaks. This important book: Describes a finite-element program, PDE2D, developed by the author over the course of 40 years Derives the ordinary and partial differential equations, with appropriate initial and boundary conditions, for a wide variety of applications Offers free access to the Windows version of the PDE2D software through the author’s website at www.pde2d.com Offers free access to the Linux and MacOSX versions of the PDE2D software also, for instructors who adopt the book for their course and contact the author at www.pde2d.com Written for graduate applied mathematics or computational science classes, Solving Partial Differential Equation Applications with PDE2D offers students the opportunity to actually solve interesting engineering and scientific applications using the accessible PDE2D.

Programming for Computations - Python

Svein Linge,Hans Petter Langtangen
Programming for Computations Python Book PDF

Author : Svein Linge,Hans Petter Langtangen
Publisher : Springer
Page : 244 pages
File Size : 55,5 Mb
Release : 2016-07-25
Category : Computers
ISBN : 9783319324289

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Programming for Computations - Python by Svein Linge,Hans Petter Langtangen Pdf

This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows the students to write simple programs for solving common mathematical problems with numerical methods in engineering and science courses. The emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.