Application of air pollution data in Klang, Selangor to find multiple roots / Nurlaila Azwa Khamsani

Many types of methods such as Halley’s and super-Halley method, modified Newton’s method, and Schroder’s method can be used in finding multiple roots of nonlinear equations. Some methods cannot be used for finding multiple roots such as Newton’s method, Bisection method, Secant method, Muller’s method, and many more. Thus, the modifications of some methods did by few researchers. This project will find the month that has highest value of mean concentration of PM10 and PM2.5 with the value of concentrations. Next, this project will be implementing the highest mean concentrations of particulate matter which are PM10 and PM2.5 in Klang as the initial guesses for finding multiple roots. Lastly, every function with different initial guess has its own best method by identifying the smallest error and smallest CPU time. For Modified Newton’s method, it is best to use on function (e-x2 — ex2 — x8 + 10)30 with initial guess 33.41. For Method 1 (M1), it is best to use on function (e-x2 — ex2 — x8 + 10)30 with initial guess 44.51, function (6x3 + 5x4 — 4x3 + 3x2 — 2x + 1)55 with initial - 2.0 and 33.41, function (ln[x2 + 3x + 5] — 2% + 7)31 for all initial guesses. Method 4 (M4) is best to use on function (e-%2 — e*2 — x8 + 10)30 with initial guess 1.3 and function (6x5 + 5x4 — 4x3 + 3x2 — 2x + 1)55 with initial guess 44.51.