Mathematical and Numerical Methods for Partial Differential Equations

Mathematical and Numerical Methods for Partial Differential Equations
Author: Joël Chaskalovic
Publisher: Springer
Total Pages: 358
Release: 2014-05-16
Genre: Mathematics
ISBN: 3319035630

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This self-tutorial offers a concise yet thorough introduction into the mathematical analysis of approximation methods for partial differential equation. A particular emphasis is put on finite element methods. The unique approach first summarizes and outlines the finite-element mathematics in general and then in the second and major part, formulates problem examples that clearly demonstrate the techniques of functional analysis via numerous and diverse exercises. The solutions of the problems are given directly afterwards. Using this approach, the author motivates and encourages the reader to actively acquire the knowledge of finite- element methods instead of passively absorbing the material as in most standard textbooks. This English edition is based on the Finite Element Methods for Engineering Sciences by Joel Chaskalovic.

Advanced Numerical Methods for Differential Equations

Advanced Numerical Methods for Differential Equations
Author: Harendra Singh
Publisher: CRC Press
Total Pages: 336
Release: 2021-07-29
Genre: Mathematics
ISBN: 1000381080

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Mathematical models are used to convert real-life problems using mathematical concepts and language. These models are governed by differential equations whose solutions make it easy to understand real-life problems and can be applied to engineering and science disciplines. This book presents numerical methods for solving various mathematical models. This book offers real-life applications, includes research problems on numerical treatment, and shows how to develop the numerical methods for solving problems. The book also covers theory and applications in engineering and science. Engineers, mathematicians, scientists, and researchers working on real-life mathematical problems will find this book useful.

Numerical Methods for Differential Equations

Numerical Methods for Differential Equations
Author: Michael Anthony Celia
Publisher:
Total Pages: 456
Release: 1992
Genre: Computers
ISBN:

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Senior/Graduate level text covering numerical methods used to solve ordinary and partial differential equations in science and engineering. Emphasis is on problem-solving as a means of gaining a deeper understanding of the fundamental concepts. Not a cookbook of formulas. Topics include an introduction to partial differential equations, finite difference method, finite element approximations, design of numerical approximations, and analytical tools. Includes review of linear algebra.

Numerical Methods for Equations and its Applications

Numerical Methods for Equations and its Applications
Author: Ioannis K. Argyros
Publisher: CRC Press
Total Pages: 476
Release: 2012-06-05
Genre: Mathematics
ISBN: 1578087538

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This book introduces advanced numerical-functional analysis to beginning computer science researchers. The reader is assumed to have had basic courses in numerical analysis, computer programming, computational linear algebra, and an introduction to real, complex, and functional analysis. Although the book is of a theoretical nature, each chapter contains several new theoretical results and important applications in engineering, in dynamic economics systems, in input-output system, in the solution of nonlinear and linear differential equations, and optimization problem.

Numerical Methods for Differential Equations

Numerical Methods for Differential Equations
Author: J.R. Dormand
Publisher: CRC Press
Total Pages: 385
Release: 2018-05-04
Genre: Mathematics
ISBN: 1351083554

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With emphasis on modern techniques, Numerical Methods for Differential Equations: A Computational Approach covers the development and application of methods for the numerical solution of ordinary differential equations. Some of the methods are extended to cover partial differential equations. All techniques covered in the text are on a program disk included with the book, and are written in Fortran 90. These programs are ideal for students, researchers, and practitioners because they allow for straightforward application of the numerical methods described in the text. The code is easily modified to solve new systems of equations. Numerical Methods for Differential Equations: A Computational Approach also contains a reliable and inexpensive global error code for those interested in global error estimation. This is a valuable text for students, who will find the derivations of the numerical methods extremely helpful and the programs themselves easy to use. It is also an excellent reference and source of software for researchers and practitioners who need computer solutions to differential equations.

Numerical Solution of Ordinary Differential Equations

Numerical Solution of Ordinary Differential Equations
Author: L.F. Shampine
Publisher: Routledge
Total Pages: 632
Release: 2018-10-24
Genre: Mathematics
ISBN: 1351427555

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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.

Numerical Analysis of Ordinary Differential Equations and Its Applications

Numerical Analysis of Ordinary Differential Equations and Its Applications
Author: Taketomo Mitsui
Publisher: World Scientific
Total Pages: 244
Release: 1995
Genre: Mathematics
ISBN: 9789810222291

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The book collects original articles on numerical analysis of ordinary differential equations and its applications. Some of the topics covered in this volume are: discrete variable methods, Runge-Kutta methods, linear multistep methods, stability analysis, parallel implementation, self-validating numerical methods, analysis of nonlinear oscillation by numerical means, differential-algebraic and delay-differential equations, and stochastic initial value problems.

Numerical Solution of Stochastic Differential Equations

Numerical Solution of Stochastic Differential Equations
Author: Peter E. Kloeden
Publisher: Springer Science & Business Media
Total Pages: 666
Release: 2013-04-17
Genre: Mathematics
ISBN: 3662126168

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The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. From the reviews: "The authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible." --ZAMP

Numerical Methods for Evolutionary Differential Equations

Numerical Methods for Evolutionary Differential Equations
Author: Uri M. Ascher
Publisher: SIAM
Total Pages: 403
Release: 2008-09-04
Genre: Mathematics
ISBN: 0898716527

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Develops, analyses, and applies numerical methods for evolutionary, or time-dependent, differential problems.