Nepal Engineering College
Changunarayan, Bhaktapur
Email: info@nec.edu.np
Subject: Numerical Methods
Teacher: Hari K. Shrestha
Subject Code: MTH 317.3
Tutorial No.: 1
Chapter Title: Solution of Non-Linear Equations
Date: June 4, 2007
1a. Using bisection method, determine one root of the equation sin (x) + x - 1 = 0 within an accuracy
of 0.001. Solve the same problem by Secant and Regula Falsi methods, using same starting
values. Compare the number of iterations required to achieve the desired results. Plot the
iteration versus absolute error for each method.
b. Find the real root of an equation x log10 x = 4.7724 by Newton-Raphson method up to six decimals
correctly. Approximate the initial guess yourself.
x

2a. Using Newton-Raphson method, find all the roots of the equation, 10 e
 x2
dx  1 with six
0
correct decimals.
b. Find one of the roots of the equation x3- 4x - 1 = 0 by fixed point iteration and bisection methods.
Carry up to 8 iterations and discuss the relative errors associated with each method.
3. The buckling load of a column, pin jointed at one end and axial force at other end, requires solution
of the transcendental equation tan x - x = 0.
  3 
 using Bisection and Regula Falsi
2 2 
Compute a real root of this equation in the interval  ,
methods, using same starting values, and compare the results in terms of percentage errors.
4. Use Newton Raphson and Fixed Point Iteration methods to find the smallest root of the equation e-x
= sin x. Carry up to 6 iterations using the same starting value, and compare the absolute errors.
5. Calculate 13 to six decimals accuracy by Newton Raphson method.
6. Find all possible roots of the equation x3 – 3x² + 7x – 8 = 0 correct to three decimal places by
Regula Falsi and Bisection methods.
7. Find where the graphs of y = x-3 and y = ln (x) intersect with bisection method. Get the intersection
value correct to four decimals.
Deadline for submission: June 14, 2007
Note: 0.2 mark out of 1 will be assigned for this tutorial.
Copying someone's answer will make both students' papers invalid.