Civil and Environmental Engineering 2219A/B Lecture Notes - Lecture 19: False Position Method, Bisection Method, Linear Interpolation

• School: Western University
• Department: Civil and Environmental Engineering
• Course: Civil and Environmental Engineering 2219A/B
• Professor: Martha Dagnew

Document Summary

Methods that systematically solve roots problem in an iterative fashion. Bracketing methods - based off two initial guesses that "bracket" the root (converge very slowly on opposite sides of the root. Open methods - based off one or more initial guesses. Doesn"t always work, but when they do, are quicker. It is very similar to bisection except it determines the next guess not by splitting the bracket in half but by connecting the endpoints with a straight line and determining the location. Using the formula shown below, based upon the graph shwon below. Where this line "the connector" intercepts the x-axis is the solution. The false position method is another bracketing method. It is also called a linear interpolation method. Choose xl and xu as two guesses for the root. If f(xl) * f(xr) < 0, then the root lies between xl and xr, then xl = xl & xu = xr.