Numerical Methods to solve equations Essay
Numerical Methods to solve equations
The table above shows the numbers of iterations each method took in order to come to the same degree of accuracy. The Newton-Raphson method was the quickest, finding the root within a certain degree of accuracy in only three iterations. Second was the Decimal Search, which took five iterations and last was the Rearrangement Method, which took the most number of iterations, 6. Newton-Raphson method is clearly the fastest and the most efficient method to use as the number of iterations needed to find a root to a degree of accuracy is small.
However, this method is very tiresome to calculate by hand and the tiniest mistake can result in a wrong answer. The Decimal Search takes more iteration; but, this method is the easiest and easily understood. However, this method is best done on a spreadsheet, where you would be able to spot the sign change easily. The Rearrangement Method takes slightly more iteration but it provides the root to any degree of accuracy. Also, the formula is iterative, therefore, it is not very time consuming. However, finding can be tricky.
In terms of the software used, Decimal Search was the easiest as it only required spreadsheet which is not difficult to use. Although making the tables can be repetitive, any faults can easily be rectified. Both the Newton-Raphson Method and the Rearrangement Method used a calculator to work out the iterative steps. This was often very time-consuming and frustrating as simple mistakes could let to the wrong route. Autograph was used to draw all the graphs and show the methods at work. It was not hard to use but tricky, due to the different options available.
University/College: University of Arkansas System
Type of paper: Thesis/Dissertation Chapter
Date: 7 July 2017