Difference Matrices for ODE and PDE: A MATLAB (R) Companion

The use of difference matrices and high-level MATLAB® commands to implement finite difference algorithms is pedagogically novel. This unique and concise textbook gives the reader easy access and a general ability to use first and second difference matrices to set up and solve linear and nonlinear systems in MATLAB which approximate ordinary and partial differential equations.

Format: Paperback / softback
Length: 204 pages
Publication date: 25 January 2023
Publisher: Springer International Publishing AG

The use of difference matrices and high-level MATLAB® commands to implement finite difference algorithms is a pedagogically novel approach. This unique and concise textbook provides the reader with easy access and a general ability to use first and second difference matrices to set up and solve linear and nonlinear systems in MATLAB, which approximate ordinary and partial differential equations.

Prerequisites include a knowledge of basic calculus, linear algebra, and ordinary differential equations. Some knowledge of partial differential equations is a plus, though the text may easily serve as a supplement for the student currently working through an introductory PDEs course. Familiarity with MATLAB is not required, though a little prior experience with programming would be helpful. In addition to its special focus on solving in MATLAB, the abundance of examples and exercises make this text versatile in use. It would serve well in a graduate course in introductory scientific computing for partial differential equations. With the prerequisites mentioned above plus some elementary numerical analysis, most of the material can be covered and many of the exercises assigned in a single semester course. Some of the more challenging exercises make substantial projects and relate to topics from other typical graduate mathematics courses, such as linear algebra, differential equations, or topics in nonlinear functional analysis. A selection of the exercises may be assigned as projects throughout the semester. The student will develop the skills to run simulations corresponding to the primarily theoretical course material covered by the instructor. The book can serve as a supplement for the instructor teaching any course in differential equations. Many of the examples can be easily implemented, and the accompanying MATLAB code can be used to verify the results.

In conclusion, this textbook is a valuable resource for students and instructors interested in learning and applying finite difference algorithms in MATLAB. Its unique approach, concise writing style, and abundance of examples and exercises make it an excellent tool for both novice and experienced users. Whether you are a student studying differential equations or an instructor looking to enhance your teaching, this textbook is a must-have.

Weight: 411g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031119996
Edition number: 1st ed. 2023