Introduction to Numerical Methods in Differential Equations

Focusing on differential equations, this book explores their critical role in science and engineering, beginning with ordinary differential equations through initial and boundary value problems. It progresses to partial differential equations involving both time and space derivatives. A significant aspect is the transformation of these equations into computable problems using numerical methods. The text emphasizes the importance of understanding discrete approximations and the impact of round-off errors in floating-point arithmetic, highlighting the potential pitfalls of seemingly correct numerical methods.