Quantitative Methods Answers

b) Solve the IVP, ; )4(y 4
x 4y
1
y
2
=
−
′ = using Euler’s method. Find )2.4(y with h = 2.0
and 1.0 and extrapolate the value )

c) Obtain the cube root of 12 using Newton-Raphson formula.

0. a) Find the solution of the difference equation yk+2 − 4yk+1 + 4yk = ;0 k = ,1,0 K. Also find
the particular solution when 1 y0 = and 6 y1 = . (2)
b) Solve the IVP, ; )4(y 4
x 4y
1
y
2
=
−
′ = using Euler’s method. Find )2.4(y with h = 2.0
and 1.0 and extrapolate the value )2.4(y . (2)
c) Solve the IVP
y 1 y , )0(y 0
2
′ = + =
using classical R-K method of h(0 )
4
. Find )4.0(y taking h = 2.0 . Compare the solution
obtained with the exact solution and find the error.

2. a) Find by Newton’s method the roots of the following equations correct to three places of
decimals.
i) log .4 772393 x 10 x = near x = 6 .
ii) f (x) = x − 2sin x near x = 2 . (4)
b) Set up the Gaussi-Jacobi iteration scheme in matrix form for the linear system of equations

4 3
4 2
4 3
2 3
1 2 3
1 2
− + =
− + − =
− =
x x
x x x
x x

Show that the iteration scheme is convergent. Hence find the rate of convergence of this
method

1. a) A negative root of smallest magnitude of the equation x 5x 20 0
3
+ + = is to be determined
i) Find an interval of unit length which contains this root
ii) Perform two iterations of the bisection method
iii) Taking the end points of the last interval as initial approximations perform one iteration
of the secant method. (5)
b) Find a root of the equation 0 3x 10x 10x 7
3 2
+ + + = which is close to − 0.2 using the
Birge-Vieta method. Perform two iterations of the method. (3)
c) Obtain the cube root of 12 using Newton-Raphson formula.

Draw a flowchart that reads the names , sex and score of each student and outputs the names of the male students that scored above 75% and how many they are?

use newton's method to approximate SQRT of 11 to 5 decimal places

The technique of determining an approximate value of f(x) for a non-tabular value of x which lies outside the internal [a, b] is known as............

For the given functions f (x), let x0 = 0, x1 = 0.6, and x2 = 0.9. Construct interpolation polynomials
of degree at most one and at most two to approximate f (0.45), and find the absolute error.
a. f (x) = cos x