Computational Methods for Partial Differential Equations by M.K. Jain is widely considered a foundational text for students and researchers in mathematics, engineering, and physics. This book provides a rigorous yet accessible bridge between theoretical analysis and the practical numerical implementation of solutions for complex physical systems.
Do not just read the equations. Use a language like Python, MATLAB, or C++ to code the finite difference schemes described in the chapters. Do not just read the equations
If you are currently working on a specific problem set or research project using this book, I can help you dive deeper. to solve a basic PDE? to solve a basic PDE
Pay close attention to the Von Neumann stability analysis sections. Understanding why a simulation "blows up" is as important as knowing how to start one. I can help you dive deeper.