This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
Comprised of six chapters, this book begins with a review of direct methods for the solution of linear systems, with emphasis on the special features of the linear systems that arise when differential equations are solved.
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, ...
0 —r 1 + 2 r We should note that the extra term in the first position of the right hand side, ruff, is obtained as the difference equation at k = 1 "reaches” to the left and gets ust". Our 0-th order treatment of the boundary condition, ...
Finite Difference Schemes and Partial Differential Equations
The book is intended for beginning graduate students and early career professionals, although advanced undergraduate students may find it equally useful.
The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.
This book is open access under a CC BY 4.0 license.
This book provides a clear summary of the work of the author on the construction of nonstandard finite difference schemes for the numerical integration of differential equations.
Praise for the First Edition ". . . fills a considerable gap in the numerical analysis literature by providing a self-contained treatment . . . this is an important work written in a clear style . . . warmly recommended to any graduate ...
This book is a detailed and step-by-step introduction to the mathematical foundations of ordinary and partial differential equations, their approximation by the finite difference method and applications to computational finance.