Question

in Java, write a program for methods (Secant, False-Position and Modified Secant) for locating roots. Make sure that you have clever checks in your program to be warned and stop if you have a divergent solution or stop if the solution is very slowly convergent after a maximum number of iterations.

(a) f(x) = 2x3 – 11.7x2 + 17.7x – 5 This function has 3 +ve roots, all of which lie between 0 and 4. Find the roots. Implement the methods until ea < 1%. Let the maximum iterations be 100. For the modified secant method, use δ = 0.01. Plot the graphs for the approximate % relative error for different roots. Each graph should have 5 error curves, one for each method.

(b) f(x) = x + 10 – xcosh(50/x) For this function, plot the % approximate relative error for each method similar to the part (a). Use δ = 0.01 for modified secant method. Figure out the initial points for the other methods. As a hint, the root lies in the interval [120, 130]

Answer 1