Solving Equations using Numerical Methods.

... A2 Pure Maths Coursework Solving Equations using Numerical Methods There are three methods with which you can solve an equation. 1. Change of Sign Method 2. Newton-Raphson Method 3. Rearranging the equation f(x)=0 in the form x= g(x) Hardware and Software Used For the coursework I have used a computer for attaining more accurate results and to avoid errors. The software I have used are * Microsoft Word * GraphCalc (A software used for drawing graphs) Change of Sign Method x4- 4x +2 We see that the roots lie in between [0, 1] and [1, 2] We confirm this by looking for a change of sign x 0 1 2 f(x) 2 -1 10 f(x) is found by substituting the values of x in the equation. We look for roots in [0, 1] x 0 0.1 0.2 0.3 0.4 0.5 0.6 f(x) 2 1.6001 1.2016 0.8081 0.4256 0.0625 -0.2704 We look for roots in [0.5, 0.6] x 0.5 0.51 0.52 f(x) 0.0625 0.02765 -0.00688 We look for roots in [0.51, 0.52] x 0.51 0.511 0.512 0.513 0.514 0.515 0.516 0.517 0.518 f(x) 0.02765 0.02418 0.02071 0.01725 0.01380 0.01034 0.00689 0.00344 -0.000002 We look for roots in [0.517, 0.518] x 0.517 0.5171 0.5172 0.5173 0.5174 f(x) 0.00344 0.00309 0.00275 0.0024 0.00206 x 0.5175 0.5176 0.5177 0.5178 0.5179 0.518 f(x) 0.00172 0.00137 0.00103 0.00068 0.00034 -0.000002 Root is in between [0.5179, 0.5180] Failure Case There are some cases where this method cannot be used to solve the equation. Newton-Raphson Method f `(x)

want to read more? →