Best Reference Books – Numerical Methods for Partial Differential Equations

We have compiled the list of Top 10 Best Reference Books on Numerical Methods For Partial Differential Equations subject. These books are used by students of top universities, institutes and colleges. Here is the full list of top 10 best books on Numerical Methods For Partial Differential Equations along with reviews.

Kindly note that we have put a lot of effort into researching the best books on Numerical Methods For Partial Differential Equations subject and came out with a recommended list of top 10 best books. The table below contains the Name of these best books, their authors, publishers and an unbiased review of books on "Numerical Methods For Partial Differential Equations" as well as links to the Amazon website to directly purchase these books. As an Amazon Associate, we earn from qualifying purchases, but this does not impact our reviews, comparisons, and listing of these top books; the table serves as a ready reckoner list of these best books.

1. “Some Topics in Nonlinear Functional Analysis” by M C Joshi and R K Bose

“Some Topics in Nonlinear Functional Analysis” Book Review: This book is clear and presents a stronger concept of complete controllability which we call Trajectory Controllability is introduced in this paper. The book provides a clear study on the Trajectory. It also emphasises Controllability of an abstract nonlinear integro-differential system in the finite and infinite dimensional space setting. It will discuss how approximations to these problems can be found computationally using finite difference methods and optimization. Examples will be presented in one, two and three dimensions.

2. “Functional Analysis and Applications” by S Kesavan

“Functional Analysis and Applications” Book Review: This book has rigorous and thorough introduction to the foundations of the subject with a clear and concise understanding. This book aims to provide a fairly complete, yet simple, treatment of the techniques from Functional Analysis used in the modern theory of Partial Differential Equations and illustrate their applications via examples. This book covers introduction to the theory of Distributions, Sobolev Spaces and Semi groups and the application of results to the study of weak solutions of elliptic boundary value problems and evolution equations. This book has four appendices at the end of each chapter and with several exercises. The book serves both as a textbook and as a source of reference for research workers in the area.

3. “Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods” by Sandip Mazumder

“Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods” Book Review: This book explains the method’s processes and techniques in careful, meticulous prose.The book focuses mainly on deterministic methods for solving partial differential equations (PDEs), namely finite difference and finite volume methods. For practical application most of the problems in the book are solved by using finite element methods in solid mechanics, and covered extensively in various other texts. The book aims to beginning graduate students and early career professionals, although advanced undergraduate students may find it equally useful. This book acts as a prerequisite for students who might go on to take additional courses in computational mechanics, computational fluid dynamics, or computational electromagnetics.

4. “Numerical Methods for Partial Differential Equations” by G Evans and J Blackledge

“Numerical Methods for Partial Differential Equations” Book Review: The book gives a clear introduction of the methods and underlying theories used in the numerical solution of partial differential equations. In this book the concepts are concise to help the students to interpret the topic in their way and to enhance their creativity. The book covers the finite difference method of parabolic or heat equations, hyperbolic or wave equations and elliptic or Laplace equations. The book emphasis is on the practical solution rather than the theoretical background, without sacrificing rigour. It has a number of examples and challenging exercises to check the understanding of the readers. This book is both for professionals and students who want a better understanding for the subject.

5. “Partial Differential Equations for Scientists and Engineers” by Stanley J Farlow

“Partial Differential Equations for Scientists and Engineers” Book Review: This book has highly useful text that shows the reader how to formulate a partial differential equation from the physical problem and how to solve the equation. This book offers realistic, practical coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems, and numerical and approximate methods. The whole book explains problems which include ‘Hyperbolic’, ‘Parabolic’ and ‘Elliptic types of equations. Each chapter contains a selection of relevant problems along with answers and suggestions for further reading. This book is for advanced undergraduate and graduate students, as well as professionals working in the applied sciences. This book has a concise exercise along with easy to understand explanations.

6. “Numerical Solution of Partial Differential Equations: Finite Difference Methods” by G D Smith

“Numerical Solution of Partial Differential Equations: Finite Difference Methods” Book Review: This book covers the standard finite difference methods of parabolic, hyperbolic, and elliptic equations, and includes the concomitant theoretical work on consistency, stability, and convergence. It also includes Lax-Richtmyer 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 along with fast-paced introduction to numerical methods. This book is for students of mathematics and engineering, and for postgraduates and professionals who need a clear, concise grounding in this discipline. This book gives a practical approach to the topic.

7. “Ordinary Differential Equations” by Morris Tenenbaum and Harry Pollard

“Ordinary Differential Equations” Book Review: This book is well-written, skillfully organized introductory text provides an exhaustive survey of ordinary differential equations. The book is simple and its step-by-step style introduces and explains the complexity of the topic. This book also defines basic terms and outlines the general solution of a differential equation-the solution that actually contains every solution of such an equation. The book deals with topics like integrating factors, dilution and accretion problems, the algebra of complex numbers, the linearization of first order systems, Laplace Transforms, Newton’s Interpolation Formulas, and Picard’s Method of Successive Approximations Legendre Differential Equation, Legendre Functions, Legendre Polynomials, the Bessel Differential Equation, and the Laguerre Differential Equation. The book contains two exceptional chapters one on series methods of solving differential equations, the second on numerical methods of solving differential equations. This book is for undergraduate students of mathematics, engineering and the sciences. It has an abundance of solved problems and practice exercises that enhance the value of the topic.

8. “Numerical Methods for Partial Differential Equations: An Introduction” by Vitoriano Ruas

“Numerical Methods for Partial Differential Equations: An Introduction” Book Review: This book is fully updated on the context and has its own unique features. This book covers the three most popular methods for solving partial differential equations: the finite difference method, the finite element method and the finite volume method. It combines the clear descriptions of the three methods, their reliability, and practical implementation aspects. It also has justification for the methods and how they work. It has a balanced emphasis both on practical considerations and a rigorous mathematical treatment. This book pays attention to low order methods, as practitioner’s overwhelming default options for everyday use along with implementation of new methods along with this can be used as a reference for the research work on numerical PDEs. This book is aimed at students of Engineering, Mathematics, Computer Science, Physics and Chemistry this book offers a substantial insight into the principles numerical methods in this class of problems are based upon.

9. “Numerical Analysis of Partial Differential Equations” by S H Lui

“Numerical Analysis of Partial Differential Equations” Book Review: This book provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The book covers the theoretical along with the numerical solution of linear systems and various examples and exercises which provides reader introduction to the essential concepts in the numerical analysis. The book focuses on topics like methods of elliptic PDEs: finite difference, finite elements, and spectral methods. The book also covers topics like the mathematical theory of elliptic PDEs, Numerical linear algebra, Numerical linear algebra, Time-dependent PDEs, Multigrid and domain decomposition, PDEs posed on infinite domains. The book concludes with a discussion of the methods for nonlinear problems. Each chapter has well defined theory and problems so as to test the understanding of the reader. This book is for the upper-undergraduate and graduate levels. The book is also suitable for students in mathematical sciences and engineering.

10. “Student Solutions Manual to Boundary Value Problems, Fifth Edition: and Partial Differential Equations” by David L Powers
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