Finite Difference Computing with PDEs by Hans Petter Langtangen
Finite Difference Computing with PDEs - Table of Contents
1. Vibration ODEs
2. Wave Equations
3. Diffusion Equations
4. Advection-Dominated Equations
5. Nonlinear Problems
A. Useful Formulas
B. Truncation Error Analysis
C. Software Engineering: Wave Equation Model
What You Will Learn in Finite Difference Computing with PDEs
"Finite Difference Computing with PDEs: A Modern Software Approach" by Hans Petter Langtangen and Svein Linge is a practical guide to solving "partial differential equations (PDEs)" using "finite difference methods". The book emphasizes hands-on learning, showing how mathematical models can be translated into efficient "Python code". It focuses on both understanding the equations and implementing them correctly in computational simulations.
The text covers a variety of classical PDEs, including "wave", diffusion, and advection-dominated equations. Each topic is presented with step-by-step derivations, clear explanations of numerical schemes, and guidance on verifying accuracy. The approach teaches readers how to design stable and reliable finite difference algorithms while highlighting common pitfalls in simulation, such as numerical errors and instability. Realistic examples from physics, biology, and engineering demonstrate how these techniques are applied to real-world problems.
Langtangen’s book is ideal for students, researchers, and professionals in "computational science", applied mathematics, and engineering. By bridging theory and practical coding skills, it equips readers to build reliable software for modeling complex systems. With its example-driven style and focus on Python implementation, this book provides a comprehensive introduction to finite difference computing, making PDEs accessible, understandable, and applicable for modern computational problems.
Book Details & Specifications
Title:
Finite Difference Computing with PDEs by Hans Petter Langtangen
Publisher:
Springer
Year:
2018
Pages:
507
Type:
PDF
Language:
English
ISBN-10 #:
3319856669
ISBN-13 #:
978-3319856667
License:
CC BY-NC 4.0
Amazon:
Amazon
About the Author: Hans Petter Langtangen
The author
Hans Petter Langtangen
was a Norwegian distinguished mathematician and computational scientist known for his expertise in "partial differential equations (PDEs)", "finite difference methods", and "scientific computing". He focused on combining mathematical theory with practical computation, helping learners and professionals tackle complex problems efficiently. Langtangen’s work "Finite Difference Computing with PDEs" is praised for its "clarity", step-by-step explanations, and computational examples. Widely used in "engineering" and "physics", it teaches numerical techniques, modeling, and simulation methods, making advanced mathematics accessible and applicable for students, researchers, and professionals working on real-world computational problems.
Read or Downloadable Finite Difference Computing with PDEs
Free Differential Equations Books PDF | Curated Academic Index