Numerical Method TU Board 2079 question paper

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 $10^{th}$ iteration.

What are the applications of interpolation? Differentiate between interpolation and regression. Consider the following data points estimate the $f(10)$ using Lagrange's interpolation. x56911y13141516

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.

Construct the divided difference table for the following data value and find first and second order derivative at $x=2$. x124810y0152127

Why it is better to use composite Simpson's $\frac{3}{8}$ rule instead of Simpson's $\frac{3}{8}$ rule? Find the value of integration for following data set using Simpson's $\frac{3}{8}$ rule. x0123456y10.50.20.10.05880.03850.027

What is least squares method of fitting a function? Fit the second order polynomial for the following data values. x1234567y2678101215

Solve the following system of linear equations using Gaussian elimination method. $2x+2y+z=12$ $3x+2y+2z=8$ $5x+10y-8z=10$

Solve the following system of linear equations using Gauss-Seidal method. $10x+y+z=12$ $2x+10y+z=13$ $2x+2y+10z=14$

Define eigen value and eigen vector. Explain how shooting method is used to solve boundary value problem.

Find the approximate value of $y$ when $x=0.6$ of $\frac{dy}{dx}=1-2xy$, given that $y=0$ when $x=0$ with $h=0.2$ using Heun's method.

Consider a steel plate of size 24cm × 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 × 8cm.

Write an algorithm for Horner's method. Evaluate the polynomial $f(x)=x^4+3x^3+5x^2+7x+9$ at $x=2$ by using Horner's method.