Numerical Methods 2024

Group B

Attempt any SIX questions.                                                                       [6*5=30]

2. Explain absolute and relative error. Find the relative error of number 5.6 if both of its digits are correct.

On what type of equations Newton's method can be applicable --Justify.

Solve the following equations by using Gauss-Jordan method. 

2x + 3y +4z = 5

3x + 4y + 5z = 6

4x + 5y + 6z = 7

Use the Romberg method to get an improved estimate of the integral from x = 1.8 to x = 3.4 from the data in the table with h = 0.4.

Write a program to compute integral    using Simpson's 1/3 rule.

Use Runge-Kutta method of 4th order solve the following equation taking each step h = 0.1 for dy/dx = [4x/y - xy] given y(0) = 3 calculate y at x = 0.1 and 0.2. 

Solve the Laplace equation Uxx + Uyy = 0 for the following square mesh with the boundary values as shown in the figure below.

Group C

Attempt any TWO questions.

Solve the given set of linear equations using Dolittle LU decomposition method:

3x1 + 2x2 + x3 = 10

2x1 +3x2 + 2x3 = 14

x1 + 2x2 + 3x3 = 14

Define initial value problems and final value problems. Using Heun's method, find value of y when x = 0.3 given that dy/dx = x+y and y = 1.

How can we use interpolation techniques (methods) to approximate the value of the integral for the functions whose antiderivatives can't be found? Explain. Wrin a program to solve  sinx -2x +1 = 0 using Bisection Method.