Numerical Method TU Board 2020 question paper

Why is the study of errors important to a computational scientist? Differentiate between inherent and numerical errors.

Find the root of equation $x^2+4x-10=0$ using bisection method where root lies between 5 and 6.

Find the square root of 3,5 using second order Lagrange interpolation polynomial using the following data table. $$\begin{array}{cccccc}x& 1& 2& 3& 4& 5\\ f(x)& 1& 1.4142& 1.7321& 2& 2.2361\end{array}$$

Write a program to calculate the integral using Trapezoidal Rule.

Solve the following set of equations using Gauss-Jordan Method. $3x-5y+2z=15$ $4xy+z=2$ $x-3y+7z=22$

Use classical Runge-Kutta method to estimate $y(0.2)$ when $y^{\prime }(x)=x^2+y^2$ with $y(0)=0$ and $h=0.2$.

Solve the Poisson equation ${\nabla }^{2}f=2x^2{y}^2$ over the square domain $0\le x\le 3$ and $0\le y\le 3$ with $f=0$ on the boundary and $h=1$.

a) Factorize the matrix $\begin{array}{ccc}1& 2& 3\\ 2& 3& 22\\ 3& 22& 82\end{array}$ Using Cholesky's method. b) Locate the root of equation $x^2+x-2$ using the fixed point method.

a) Fit a straight line to the following set of data points.$x$134689$y$134457 b) Differentiate between ordinary and partial differential equations with their applications.

Given the data points: $i$012$x_i$234$f_i$4916Estimate the function value $f$ at $x=2.5$ using cubic splines.