What are the applications of interpolation? Differentiate between interpolation and regression. Consider the following data points estimate the $f(10)$ using Lagrange's interpolation.
What do you mean by numerical integration? Write any one application of numerical integration. Write an algorithm and c program to implement multi-segment trapezoidal rule. [10]
2.
Construct the divided difference table for the following data value and find first and second order derivative at x=2.
Why it is better to use composite simpson's 3/8 rule instead of simpson's 3/8 rule? Find the value of integration for following data set using simpson's 3/8 rule.
Define true error and relative error. Derive the bisection method for solving non-linear equation and using this method solve $2x^3-2x-5$ with initial $x_0=1$ and $x_1=2$. Calculate upto 10th iteration. [10]
2.
Write an algorithm for Honer's method. Evaluate the polynomial $f(x) = x^4 + 3x^3 + 5x^2 + 7^x + 9$ at x = 2 by using Honer's method. [5]
Solution of Ordinary Differential Equations
1.
Find the approximate value of y when x = 0.6 of $dy/dx = 1-2xy$, given that y = 0 when x = 0 with h=0.2 using Heun's method. [5]
Solution of Partial Differential Equations
1.
Consider a steel plate of size 24cm x 24cm. If two of the opposite sides are held at 100 degree Celsius and the other two opposite sides at 0 degree Celsius, find the steady state temperatures of interior points, assuming a grid size of 8cm x 8cm. [5]
Solving System of Linear Equations
1.
Solve the following system of linear equations using Gaussian elimination method. $2x+2y+z=12$, $3x+2y+2z=8$, $5x+10y-8z=10$ [5]
2.
Solve the following system of linear equations using Gauss-Seidal method. $10x+y+z=12$, $2x+10y+z=13$, $2x+2y+l0z=14$ [5]
3.
Define eigen value and eigen vector. Explain how shooting method is used to solve boundary value problem. [5]