Around 1650 B.C. the Egyptians numerically used an algorithm to find the roots of simple equations. Greeks, including Archimedes, used repetitive algorithms to solve geometric problems around 250 B.C.. In the 1600s Newton and Leibnitz discovered calculus. With calculus came a large base of numerical techniques. These techniques, like the Newtonian method of approximating roots using a repetitive algorithm using derivatives, are still used in modern-day computational numerical analysis, albeit employing a computer.
Since the development of the electronic computer in the 20th century the field of computational numerical analysis has boomed. While algorithms have been around for approximating the solutions of continuous problems have been around for more than 3,000 years, they were extremely tedious and very slow to use. Today, a modern computer measures in microseconds what in days gone by would have required months of work to complete.
You can use computational numerical analysis to approximate a solution to a myriad of continuous problems in mathematics. The fields are too numerous to list here but numerical techniques are especially useful in processing differential equations. Differential equations have a multitude of applications in business, engineering, science and economics. The practitioners of these fields are interested in real-world solutions rather than dreamy math theory, and you can obtain these practical solutions using computational numerical analysis.