Numerical Methods for Partial Differential Equations by William F. Ames (PDF)

Description

Numerical Methods for Partial Differential Equations, Second Edition deals with the use of numerical methods to solve partial differential equations. In addition to numerical fluid mechanics, hopscotch and other explicit-implicit methods are also considered, along with Monte Carlo techniques, lines, fast Fourier transform, and fractional steps methods. Comprised of six chapters, this volume begins with an introduction to numerical calculation, paying particular attention to the classification of equations and physical problems, asymptotics, discrete methods, and dimensionless forms. Subsequent chapters focus on parabolic and hyperbolic equations, elliptic equations, and special topics ranging from singularities and shocks to Navier-Stokes equations and Monte Carlo methods. The final chapter discuss the general concepts of weighted residuals, with emphasis on orthogonal collocation and the Bubnov-Galerkin method. The latter procedure is used to introduce finite elements.This book should be a valuable resource for students and practitioners in the fields of computer science and applied mathematics.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Nice book, arrived as expected in good condition in good time. We use this book for my numerical partial differential equations course.

⭐This book is very detail on how to generate numerical methods for partial differential equations. Staring from basics, the author proceeds with detailed examples and more complicated ideas. This is book will be very helpful for the people having basic computational knowledge and scientific computing experience.But the book is written in 1977. Some difficult ideas will be easier to be implemented on large scale computers such as Linux clusters or SGI machines. I also found one small shortcoming is that the problem complexity is not detailed discussed. This will be very important now for comparing different algorithms to accomplish the same problem.

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