Environmental Methods Essay

ME310 NUMERICAL METHODS
PROGRAMMING PROJECT 1
TABLE OF CONTENTS
1. TABLE OF CONTENTS -------------------------------------------------------------------------------------------------1
2. INTRODUCTION --------------------------------------------------------------------------------------------------------2
3.NECESSARY HAND CALCULATION-----------------------------------------------------------------------------------2
4.FORMULATIONS USED IN THE CALCULATION--------------------------------------------------------------------3
5.NUMERICAL RESULTS --------------------------------------------------------------------------------------------------3
6.PLOTTED GRAGHICS----------------------------------------------------------------------------------------------------4

Both Methods reaches the result demanded fast. On Figure 3, approximate errors decreases suddenly and reaches the with 5 for Secant Method, the graph shows the 7 iteration because of 2 initial guesses, that is, the code count the 2 initial guesses as first 2 iteration.. On the other hand, On Figure 5, approximate errors decreases like Figure 3 andreaches to the value which is defined by user with in 6 iterations, because, our function count y1 as a first iteration. This results shows us the Secant Method is more succesful than the Quadratic Method as expressed at the end of the code. That is, the code finally decide which method achieve the result faster.
There is also an important points for both formula. The secant method has on its denominator and the quadratic method has square root as and denominator as . The user is warned by the code before the initial guesses about the no result or complex result could be obtained due to zero denominator or negative value in the square