2nd Assignment of Numerical Methods in Engineering (ME 309)

Beant College of Engineering & Technology Gurdaspur

5^th Semester Mech (Section A&B)

2^nd  Assignment of  Numerical Methods in Engineering (ME 309) (10 Marks)

Due date: In the week starting 06/08/12 during respective Tutorials.

Q1.      Use bisection method to find square root of 30, correct up to 4 decimal places.

Q2.      Using bisection method, find the real root of the equation f(x) = 3x – (1 + sin x)^1/2 = 0, correct up to 3 decimal places.

Q3.      Find the real root of the equation f(x) = xe^x – 3 = 0, using Regula Falsi (false position) method, correct up to 3 decimal places.

Q4.      Find the real root of the equation f(x) = x² – log_e x – 3 = 0, using Regula Falsi (false position) method, correct up to 3 decimal places.

Q5.      Find the approximate root of the equation f(x) = e^-x – sin x  = 0, using Newton-Raphson  method, correct up to 4 decimal places. Start at x₀ = 0.6.

Q6.      Find the real root of the equation f(x) = 3x – cos x – 1 = 0, using Newton-Raphson method, correct up to 4 decimal places.

Q7.      The root of the equation f(x) = sin x – 5x – 2 = 0, lies near 0.5. This equation can be written in two possible ways to find its root by iterative method. Which of two possible ways will not yield result and which one will yield result and hence find the root of the equation correct up to four decimal places?

Q8.      Find the root of the equation f(x) = xe^x = 0, correct up to three decimal places using secant method.

Q9.      Find the root of the equation f(x) = 5x – cos  x – 3  =  0, correct up to three decimal places using Aitken’s Δ² method.