False Position Method.pptx

Numerical methods

1. NUMERICAL METHODS TOPIC 2: REGULI-FALSI (FALSE POSITION) METHOD

2. REGULI-FALSI (FALSE POSITION) The REGULI-FALSI method (also known as False Position linear-interpolation method) involves obtaining values for two roots to the equation f(x)=0 by trial-and-error. In this method, the nonlinear function f(x) is assumed to be a linear function g(x) in the interval ( a,b ), and the root of the function g(x) , x=c , is taken as the next approximation of the root of the nonlinear equation function f(x), x= The method is called linear interpolation method.  

3.         g         The nonlinear function f(x) is assumed to be a linear function g(x) in the interval ( a,b ), and the root of the function g(x) , x=c , is taken as the next approximation of the root of the nonlinear equation function f(x), x=  

4. REGULI-FALSI (FALSE POSITION) The root of the linear equation function g(x), that is x=c, is not the root of the linear function f(x). It is a false position (in Latin, Regula Falsi ), which gives the method its name. We now have two interval ( a,c ) and ( c,b ). As in the bisection method, the interval containing the root of the nonlinear function f(x) is retained.

5. REGULI-FALSI (FALSE POSITION) The equation of the linear function g(x) is: Where f(c)=0, the equation will be: or  

6. REGULI-FALSI (FALSE POSITION) Consider the four-bar linkage, the relationship between and can be obtained by using the formula:   At determine , at min =30 deg and max = 40 deg. Convergence criterion is  

7. REGULI-FALSI (FALSE POSITION) Look for recent study/innovation on the application of Reguli- Falsi in your specific field. Summary shall be submitted in 1 page No duplication