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Title Numerical Solution of Partial Differential Equations in Science and Engineering
Author Leon Lapidus
Publisher John Wiley & Sons
Release 2011-02-14
Category Mathematics
Total Pages 677
ISBN 1118031210
Language English, Spanish, and French
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Book Summary:

From the reviews of Numerical Solution of PartialDifferential Equations in Science and Engineering: "The book by Lapidus and Pinder is a very comprehensive, evenexhaustive, survey of the subject . . . [It] is unique in that itcovers equally finite difference and finite element methods." Burrelle's "The authors have selected an elementary (but not simplistic)mode of presentation. Many different computational schemes aredescribed in great detail . . . Numerous practical examples andapplications are described from beginning to the end, often withcalculated results given." Mathematics of Computing "This volume . . . devotes its considerable number of pages tolucid developments of the methods [for solving partial differentialequations] . . . the writing is very polished and I found it apleasure to read!" Mathematics of Computation Of related interest . . . NUMERICAL ANALYSIS FOR APPLIED SCIENCE Myron B. Allen andEli L. Isaacson. A modern, practical look at numerical analysis,this book guides readers through a broad selection of numericalmethods, implementation, and basic theoretical results, with anemphasis on methods used in scientific computation involvingdifferential equations. 1997 (0-471-55266-6) 512 pp. APPLIED MATHEMATICS Second Edition, J. David Logan.Presenting an easily accessible treatment of mathematical methodsfor scientists and engineers, this acclaimed work covers fluidmechanics and calculus of variations as well as more modernmethods-dimensional analysis and scaling, nonlinear wavepropagation, bifurcation, and singular perturbation. 1996(0-471-16513-1) 496 pp.

Title Numerical Solution of Partial Differential Equations
Author Gordon D. Smith
Publisher Oxford University Press
Release 1985
Category Mathematics
Total Pages 337
ISBN 9780198596509
Language English, Spanish, and French
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Book Summary:

Substantially revised, this authoritative study covers the standard finite difference methods of parabolic, hyperbolic, and elliptic equations, and includes the concomitant theoretical work on consistency, stability, and convergence. The new edition includes revised and greatly expanded sections on stability based on the Lax-Richtmeyer definition, the application of Pade approximants to systems of ordinary differential equations for parabolic and hyperbolic equations, and a considerably improved presentation of iterative methods. A fast-paced introduction to numerical methods, this will be a useful volume for students of mathematics and engineering, and for postgraduates and professionals who need a clear, concise grounding in this discipline.

Title Numerical Methods for Elliptic and Parabolic Partial Differential Equations
Author Peter Knabner
Publisher Springer Nature
Release 2021-11-19
Category Mathematics
Total Pages 802
ISBN 3030793850
Language English, Spanish, and French
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Book Summary:

This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.

Title Partial Differential Equations with Numerical Methods
Author Stig Larsson
Publisher Springer Science & Business Media
Release 2008-12-05
Category Mathematics
Total Pages 262
ISBN 3540887059
Language English, Spanish, and French
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Book Summary:

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.

Title Numerical Methods for Partial Differential Equations
Author Vitoriano Ruas
Publisher John Wiley & Sons
Release 2016-08-22
Category Technology & Engineering
Total Pages 300
ISBN 1119111358
Language English, Spanish, and French
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Book Summary:

Numerical Methods for Partial Differential Equations: An Introduction Vitoriano Ruas, Sorbonne Universités, UPMC - Université Paris 6, France A comprehensive overview of techniques for the computational solution of PDE's Numerical Methods for Partial Differential Equations: An Introduction covers the three most popular methods for solving partial differential equations: the finite difference method, the finite element method and the finite volume method. The book combines clear descriptions of the three methods, their reliability, and practical implementation aspects. Justifications for why numerical methods for the main classes of PDE's work or not, or how well they work, are supplied and exemplified. Aimed primarily at students of Engineering, Mathematics, Computer Science, Physics and Chemistry among others this book offers a substantial insight into the principles numerical methods in this class of problems are based upon. The book can also be used as a reference for research work on numerical methods for PDE’s. Key features: • A balanced emphasis is given to both practical considerations and a rigorous mathematical treatment. • The reliability analyses for the three methods are carried out in a unified framework and in a structured and visible manner, for the basic types of PDE's. • Special attention is given to low order methods, as practitioner's overwhelming default options for everyday use. • New techniques are employed to derive known results, thereby simplifying their proof. • Supplementary material is available from a companion website.

Partial Differential Equations by Mark S. Gockenbach

Title Partial Differential Equations
Author Mark S. Gockenbach
Publisher SIAM
Release 2010
Category Mathematics
Total Pages 654
ISBN 0898719488
Language English, Spanish, and French
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Book Summary:

Partial differential equations (PDEs) are essential for modeling many physical phenomena. This undergraduate textbook introduces students to the topic with a unique approach that emphasizes the modern finite element method alongside the classical method of Fourier analysis.

Title Numerical Partial Differential Equations
Author J.W. Thomas
Publisher Springer Science & Business Media
Release 2013-11-27
Category Mathematics
Total Pages 556
ISBN 1461205697
Language English, Spanish, and French
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Book Summary:

Continuing the theme of the first, this second volume continues the study of the uses and techniques of numerical experimentation in the solution of PDEs. It includes topics such as initial-boundary-value problems, a complete survey of theory and numerical methods for conservation laws, and numerical schemes for elliptic PDEs. The author stresses the use of technology and graphics throughout for both illustration and analysis.

Title Advanced Topics in Computational Partial Differential Equations
Author Hans Petter Langtangen
Publisher Springer Science & Business Media
Release 2012-09-22
Category Mathematics
Total Pages 663
ISBN 3642182372
Language English, Spanish, and French
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Book Summary:

A gentle introduction to advanced topics such as parallel computing, multigrid methods, and special methods for systems of PDEs. The goal of all chapters is to ‘compute’ solutions to problems, hence algorithmic and software issues play a central role. All software examples use the Diffpack programming environment - some experience with Diffpack is required. There are also some chapters covering complete applications, i.e., the way from a model, expressed as systems of PDEs, through to discretization methods, algorithms, software design, verification, and computational examples. Suitable for readers with a background in basic finite element and finite difference methods for partial differential equations.

Title Numerical Methods for Elliptic and Parabolic Partial Differential Equations
Author Peter Knabner
Publisher Springer Science & Business Media
Release 2003-06-26
Category Mathematics
Total Pages 426
ISBN 038795449X
Language English, Spanish, and French
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Book Summary:

This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.

Title Numerical Methods for Partial Differential Equations
Author You-lan Zhu
Publisher Lecture Notes in Mathematics
Release 1987-12-17
Category Mathematics
Total Pages 244
ISBN
Language English, Spanish, and French
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Book Summary:

These Proceedings of the first Chinese Conference on Numerical Methods for Partial Differential Equations covers topics such as difference methods, finite element methods, spectral methods, splitting methods, parallel algorithm etc., their theoretical foundation and applications to engineering. Numerical methods both for boundary value problems of elliptic equations and for initial-boundary value problems of evolution equations, such as hyperbolic systems and parabolic equations, are involved. The 16 papers of this volume present recent or new unpublished results and provide a good overview of current research being done in this field in China.