Buy new:
-24% $98.39
FREE delivery Monday, May 20
Ships from: Amazon.com
Sold by: Amazon.com
$98.39 with 24 percent savings
List Price: $130.00

The List Price is the suggested retail price of a new product as provided by a manufacturer, supplier, or seller. Except for books, Amazon will display a List Price if the product was purchased by customers on Amazon or offered by other retailers at or above the List Price in at least the past 90 days. List prices may not necessarily reflect the product's prevailing market price.
Learn more
FREE Returns
In Stock
$$98.39 () Includes selected options. Includes initial monthly payment and selected options. Details
Price
Subtotal
$$98.39
Subtotal
Initial payment breakdown
Shipping cost, delivery date, and order total (including tax) shown at checkout.
Ships from
Amazon.com
Ships from
Amazon.com
Sold by
Amazon.com
Sold by
Amazon.com
Returns
30-day easy returns
30-day easy returns
This item can be returned in its original condition for a full refund or replacement within 30 days of receipt.
Read full return policy
Returns
30-day easy returns
This item can be returned in its original condition for a full refund or replacement within 30 days of receipt.
Read full return policy
Payment
Secure transaction
Your transaction is secure
We work hard to protect your security and privacy. Our payment security system encrypts your information during transmission. We don’t share your credit card details with third-party sellers, and we don’t sell your information to others. Learn more
Payment
Secure transaction
We work hard to protect your security and privacy. Our payment security system encrypts your information during transmission. We don’t share your credit card details with third-party sellers, and we don’t sell your information to others. Learn more
$81.92
Pages include notes, underlining, or highlighting. May have some shelf-wear due to normal use. Your purchase funds free job training and education in the greater Seattle area. Thank you for supporting Goodwill's nonprofit mission! Pages include notes, underlining, or highlighting. May have some shelf-wear due to normal use. Your purchase funds free job training and education in the greater Seattle area. Thank you for supporting Goodwill's nonprofit mission! See less
$3.99 delivery Wednesday, May 22. Details
Or fastest delivery May 17 - 21. Details
Only 1 left in stock - order soon.
$$98.39 () Includes selected options. Includes initial monthly payment and selected options. Details
Price
Subtotal
$$98.39
Subtotal
Initial payment breakdown
Shipping cost, delivery date, and order total (including tax) shown at checkout.
Access codes and supplements are not guaranteed with used items.
Ships from and sold by Seattlegoodwill.
Kindle app logo image

Download the free Kindle app and start reading Kindle books instantly on your smartphone, tablet, or computer - no Kindle device required.

Read instantly on your browser with Kindle for Web.

Using your mobile phone camera - scan the code below and download the Kindle app.

QR code to download the Kindle App

Follow the author

Sandip Mazumder Ph.D.
+ Follow
More books from this author
Something went wrong. Please try your request again later.

Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods 1st Edition

by Sandip Mazumder Ph.D. (Author)
5.0 5.0 out of 5 stars 5 ratings
See all formats and editions
{"desktop_buybox_group_1":[{"displayPrice":"$98.39","priceAmount":98.39,"currencySymbol":"$","integerValue":"98","decimalSeparator":".","fractionalValue":"39","symbolPosition":"left","hasSpace":false,"showFractionalPartIfEmpty":true,"offerListingId":"mRw%2B1L35wHamLRb4I%2BS%2FFc0jcJ5j6cSZDHADkFBzXhkesEA1SjLYnz1SukTtcNjkFIgsBratgwuGHsz7LBOSHuDzCk4M2%2BlMIbJcg20ddOrgJZtHx7bbe%2FfZi3FyH9RRBKayRabPjFRX3jhCyNuuVw%3D%3D","locale":"en-US","buyingOptionType":"NEW","aapiBuyingOptionIndex":0}, {"displayPrice":"$81.92","priceAmount":81.92,"currencySymbol":"$","integerValue":"81","decimalSeparator":".","fractionalValue":"92","symbolPosition":"left","hasSpace":false,"showFractionalPartIfEmpty":true,"offerListingId":"mRw%2B1L35wHamLRb4I%2BS%2FFc0jcJ5j6cSZ1VbUadVCaGfEN4hY39VePRhrWMXjwRCiOTv6uP4Rp8nSzdxZe9tax4OKsxGAk3TJYEolQzO7nM%2FdjVmZsVp1zbO%2FQBPqR0%2FuJ1VRFwjNyGq0gXvObc9M9S0oJYcABvpb9YLnXa4fOddgHaKNr1DZ4gRVmgw3s9ui","locale":"en-US","buyingOptionType":"USED","aapiBuyingOptionIndex":1}]}

Purchase options and add-ons

Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods focuses on two popular deterministic methods for solving partial differential equations (PDEs), namely finite difference and finite volume methods. The solution of PDEs can be very challenging, depending on the type of equation, the number of independent variables, the boundary, and initial conditions, and other factors. These two methods have been traditionally used to solve problems involving fluid flow.

For practical reasons, the finite element method, used more often for solving problems in solid mechanics, and covered extensively in various other texts, has been excluded. The book is intended for beginning graduate students and early career professionals, although advanced undergraduate students may find it equally useful.

The material is meant to serve as a prerequisite for students who might go on to take additional courses in computational mechanics, computational fluid dynamics, or computational electromagnetics. The notations, language, and technical jargon used in the book can be easily understood by scientists and engineers who may not have had graduate-level applied mathematics or computer science courses.

  • Presents one of the few available resources that comprehensively describes and demonstrates the finite volume method for unstructured mesh used frequently by practicing code developers in industry
  • Includes step-by-step algorithms and code snippets in each chapter that enables the reader to make the transition from equations on the page to working codes
  • Includes 51 worked out examples that comprehensively demonstrate important mathematical steps, algorithms, and coding practices required to numerically solve PDEs, as well as how to interpret the results from both physical and mathematic perspectives
Read more Read less
Previous page
  1. ISBN-10
    0128498943
  2. ISBN-13
    978-0128498941
  3. Edition
    1st
  4. Publisher
    Academic Press
  5. Publication date
    January 2, 2016
  6. Language
    English
  7. Dimensions
    7.52 x 1.09 x 9.25 inches
  8. Print length
    484 pages
  9. See all details
Next page
Amazon First Reads | Editors' picks at exclusive prices

Editorial Reviews

Review

"All in all, this is a good book for the engineering students being patient enough to study this exciting and advanced subject of numerically solving PDEs. These students will be able to analyse their computational results, compare them for several methods and use to judge on them since not all what the computer prints or draws is useful information." --Zentralblatt MATH

"The book is rich in examples and numerical results. Each chapter contains exercises. The book could be a valuable text for engineering students." --Mathematical Reviews

Review

A thorough step-by-step guide for graduate students and practicing engineers on the fundamental techniques, algorithms, and coding practices required for solving PDEs using the finite difference and finite volume methods

Product details

  • Publisher ‏ : ‎ Academic Press; 1st edition (January 2, 2016)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 484 pages
  • ISBN-10 ‏ : ‎ 0128498943
  • ISBN-13 ‏ : ‎ 978-0128498941
  • Item Weight ‏ : ‎ 2.2 pounds
  • Dimensions ‏ : ‎ 7.52 x 1.09 x 9.25 inches
  • Customer Reviews:
    5.0 5.0 out of 5 stars 5 ratings

About the author

Follow authors to get new release updates, plus improved recommendations.
Sandip Mazumder Ph.D.

Sandip Mazumder Ph.D.

Brief content visible, double tap to read full content.
Full content visible, double tap to read brief content.

Sandip Mazumder was born in Calcutta (Kolkata), India. Following his bachelor’s degree in Mechanical Engineering from the Indian Institute of Technology, Kharagpur, he started his graduate education in the autumn of 1991. In 1997, he graduated with a Ph.D. in Mechanical Engineering from the Pennsylvania State University. After graduation, he joined CFD Research Corporation, where he was one of the architects and early developers of the commercial computational fluid dynamics code CFD-ACE+. In 2004, he joined the Ohio State University, where he is currently a full professor. Dr. Mazumder is the author of a graduate-level textbook entitled Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods (Academic Press, 2016), and more than 70 journal articles. He is the recipient of the McCarthy award for teaching and the Lumley award for research from the Ohio State College of Engineering among many other awards, and is also a Fellow of the American Society of Mechanical Engineers (ASME) since 2011.

Customer reviews

5 out of 5 stars
5 out of 5
5 global ratings

Top reviews from the United States

CashRajaster
5.0 out of 5 stars Thorough but writing could be more organized.
Reviewed in the United States on August 28, 2021
The book is supplemented with a series of YouTube lectures by the author, Dr. Mazumder, from Ohio State. Watching the lectures after or before reading the corresponding is to great avail and benefit. The exercises in the book are logically introduced to build up the cannon. I didn’t keep the book as it was available online for free. And there is a Facebook page with errata included.

It is rigorous and highly recommend.
One person found this helpful
Helpful
 Report
SeferTech
5.0 out of 5 stars An excellent choice for a main textbook for course in numerical methods for PDEs...
Reviewed in the United States on February 20, 2018
Chapter 1
Numerical methods are needed to solve partial differential equations (PDEs). This is because many mathematical models of physical phenomena result in one or more coupled PDEs which are usually non-linear and therefore not easily solved analytically. Focusing on second-order PDEs, which are commonly seen in science and engineering, there are two ways to classify them. One is based on the number of directions in the space of the independent variables along which the solution and/or its derivatives may be discontinuous. By considering the discriminant of the coefficients of the PDE, it can be classified as either elliptic (0 directions), parabolic (1 direction), or hyperbolic (2 directions). Another way to classify PDEs is by considering either equilibrium (steady state; elliptic) or marching (unsteady; parabolic or hyperbolic) problems. The later classification is useful regarding the choice of numerical method (iterative for elliptic vs. marching for parabolic/hyperbolic). Numerous examples are brought including the classical Laplace, heat, and wave equations all the way up to the Navier-Stokes equations for fluid dynamics.

Regarding numerical methods and the discretization of the physical domain and PDE to be solved, finite-difference methods (FDM), finite-volume methods (FVM), and finite-element methods (FEM) are quickly overviewed. In FDM, the derivatives appearing in the original PDE are replaced (approximated) by finite-difference formulas derived from manipulated and truncated Taylor series expansions resulting in a set of discrete algebraic equations governing the dependent variable evaluated at a series of grid or mesh points (not necessarily uniformly spaced) over the physical domain (now the computational domain) of the problem of interest.

In FVM, the physical domain is discretized into a series of non-overlapping control volumes of structured or unstructured shape producing the computational domain and the original PDE is integrated over each of the control volumes. Volumetric derivatives associated with terms involving the divergence of the dependent variable or some function thereof are converted using Gauss’s Divergence Theorem to integrals over the bounding surface of the elements. These surface integrals often require evaluation of the so-called physical flux of the quantity of interest on the cell boundaries resulting in a set of discrete (or semi-discrete in the case of unsteady PDEs) algebraic equations for each cell which can be solved to yield the cell volume average (evaluated at the cell centroid) of the dependent variable of interest.

In FEM, we discretize the domain in the same fashion as in FVM e.g. into elements. Then we multiply the PDE of interest by a smooth test function and then integrate over each of the finite elements. Next the dependent variable is expressed as a weighted sum of known basis functions. The test function is also written as a similar weighted sum (with different weights) of basis functions. For the standard Galerkin method the basis functions for the solution and the test function are chosen to be the same. Substitution of these forms into the integrated PDE yields a set of discrete algebraic equations for the unknown expansion coefficients whose solution enables one to evaluate the solution to the PDE. The basis functions are like the skeleton or muscles of the solution.

In all three methods, implementation of boundary conditions, whether Dirichlet (setting the dependent variable itself on the boundary), Neumann (setting the gradient normal to the boundary), or Robin (setting a linear combination of the dependent variable and its derivative on the boundary), must be done with care. The author has an excellent recent article on this which you can find here (http://heattransfer.asmedigitalcollection.asme.org/article.aspx?articleID=2598730).

The bottomline for all three methods is that they result in a set of discrete algebraic equations for the solution which must be solved. This will begin to be addressed in the next and subsequent chapters.

The chapter ends with a discussion of different mesh types used in all three methods including structured Cartesian grids, body-fitted curvlinear grids, and unstructured grids and some of the advantages and disadvantages of each method when it comes to handling complex geometries. Finally, there is a nice qualitative discussion of verification and validation efforts in solving PDEs numerically.

Overall, an excellent jam packed chapter that provides a nice overview of the major numerical methods for solving PDEs. There are also nice end of the chapter exercises to gain hands-on experience.

Chapter 2
The subject of this chapter is finite-difference methods for boundary value problems. The initial focus is 1D and after discretization of space (grid generation), introduction of stencil notation, and Taylor series expansions (including detailed derivations), the simple 2nd-order central difference finite-difference equation results. The truncation or discretization error is identified as second-order in this case. There is a considerable focus on all implementation of three types of boundary conditions including numerical examples. Finally, the nodal equations are assembled into matrix form including pseudocode to form the coefficient matrix and right-hand-side vectors. Finally, an extension to multidimensions is presented including valuable pseudocode (that works!) for generating the matrix system. The chapter concludes with a brief discussion of high-order approximations, extension to cylindrical coordinate systems, and finally transformation to curvilinear coordinate system which is very valuable and unique to textbooks of this type.

Chapter 3
After setting up systems of linear algebraic equations arising from finite-difference approximations to PDEs in the previous chapter, Chapter 3 focuses appropriately on their solution. This is broken up into the usual direct vs. Iterative methods distinction. Gauss elimination is treated in detail including pseudocode (that works!) with careful attention to local vs. global notation. Tridiagonal and pentadiagonal matrix solvers are presented next complete with pseudocode. Iterative solvers are up next including Jacobi, Gauss-Seidel in point and line forms, and followed by Stone’s strongly implicit method (not usually detailed in texts like this). After this nice and clear (light on math) presentations of method of steepest descent and conjugate gradient method follow with pseudocode and nice illustrative examples and figures. A unique feature of the book addresses the issue of non-linear source terms and how to handle them wraps up the solidly written and presented chapter.

Chapter 4
Chapter 4 focuses on stability and convergence of iterative solvers addressing eigenvalues and condition numbers of iterative matrices and diagonal dominance. The Fourier decomposition of errors is nicely presented in full details leading to the definition of the spectral radius of convergence, preconditioning, and eventually multigrid methods to accelerate convergence. Both geometric and algebraic multigrid methods are presented in full details with pseudocode (that works!) with the later rarely presented in texts of this type.

Chapter 5
It’s time for time! Here parabolic and hyperbolic PDEs and time marching is covered. For parabolic PDEs, the classical explicit, implicit and Crank-Nicolson trifecta are presented clearly complete with stability analysis. Time-splitting alternate direction implicit method is also covered. This is all pretty basic and not very exciting but for a first course it is well done. For hyperbolic PDEs, the classical 2nd order wave equation is treated in much the same way e.g. explicit, implicit and Crank-Nicolson. Finally, higher order methods for ODEs are presented such as Runge-Kutta and Adams methods motivated by the semi-discrete approach to solving PDEs. This ends the presentation of FDM and the next chapter will tackle FVM.

Chapter 6
This is where the book really shines! It presents the FVM from scratch and clearly states the goal of determining volume-averaged values at cell centroids and introducing key notation such as cell face, cell center, and nodes. It begins with 1D steady problems and through a formal derivation of the FVM clearly defines and emphasizes the importance of local and global flux conservation and boundary condition implementation. Advection-diffusion equations are treated next. For pure diffusion equations the key is discrete approximation comes involves the derivative or flux at the cell edge. When advection is present, discrete approximates for the dependent variable itself at the cell edge is required allowing for the possibly of upwinding and the important grid Peclet number. Upwinding schemes are extensively presented from basic upwind to exponential to QUICK. Extension of FVM to multidimensions is next with full details and examples. Then axisymmetric problems are treated followed by a presentation of FVM in curvilinear coordinates. The chapter ends with a nice comparison of FDM and FVM.

Chapter 7

This is the reason I selected this book as the main text for my class. It deals with the unstructured FVM. It begins with a presentation of Gauss-Divergence theorem and discussion of the diffusive flux. Then a detailed presentation of unstructured grid stencil with clearly labeled notation will set the stage for implementation of FVM on unstructured grids. Emphasis on processing and storage of geometric (mesh) information, processing connectivity information (Figure 7.3 is my favorite in the entire text), and pseudocode. Interpolation to determine face center and nodal values from cell centers (which are all you have to work with) is presented next. A key realisation we had in class was how nodal values are needed for evaluating cell edge fluxes. Calculation of cell volumes, face areas, and surface normals are presented in implementable detail including pseudocode. Treatment of normal and tangential fluxes follow. Extension to 3D, treatment of boundary conditions, construction of matrix system, and extension to advection-diffusion finish up this unique and well written chapter. It is worth the price of the book just to study this chapter and all its details.

Chapter 8

This chapter surprised me. It is called miscellaneous topics making me think it could be skipped. A careful study of this chapter shows it is anything but miscellaneous. It is strategically placed and highly relevant to the rest of the book. It deals with traditional numerical methods topics such as interpolation, numerical integration, and solving non-linear algebraic equations. The second half of the chapter is where the author tie’s these topics into the rest of the book. A very nice presentation of the use of Newton-Raphson method for solving non-linear algebraic equation systems is followed by an illustration of how this is used to handle non-linear PDEs. Finally, while solving one PDE at a time is nice, in practice coupled PDEs usually need to be solved for most science and engineering problems. This is dealt with in the last section of the chapter and the book complete with a very nice detailed example.

Overall review

Overall, this is an excellent textbook for a first course in numerical methods for PDEs which focuses on the most popular methods of finite-difference and finite-volume methods. It is unique in that it present useful pseudocode and emphasizes details of unstructured finite-volume methods - which is rare to find in such a book. After finishing the book, we had some extra time to introduce spectral methods, method of weighted residual, and discontinuous Galerkin (DG) methods (although I would probably leave DG methods for an advanced class next time). My postdoc wrote a very nice Python code to implement the pseudocode in Chapter 7 for unstructured FVM for solving 2D diffusion and advection-diffusion PDEs. A few students in the class used this code (which relied on the open source grid generation gmsh) for their final class project to good effect. Perhaps we will share this code with the community in future posts. Happy coding!
4 people found this helpful
Helpful
 Report