1. Numerical Methods Foundations

Introduction to Numerical Methods 

Numerical methods are mathematical techniques used to formulate problems so they can be solved with arithmetic operations. While analytical methods provide exact, continuous solutions (like finding the exact integral of a function using calculus), numerical methods provide approximate, discrete solutions.

These techniques are the backbone of modern computational engineering. When analyzing complex systems—such as modeling rainfall runoff in a watershed or performing finite element analysis on a structure—analytical solutions are often impossible. Numerical methods allow computers to process these complex spatial and physical models by breaking them down into manageable arithmetic calculations.

ERRORS AND THEIR COMPUTATIONS

A GENERAL ERROR FORMULA