Numerical Method old question papers

Explain how Newton-Raphson method differs from bisection method. Derive the formula for Newton-Raphson method. Use bisection method to solve $x^3-x-2=0$ in $1<x<2$.

Write an algorithm and program to compute interpolation using Newton's backward interpolation.

Explain the power method for finding eigen value. Differentiate between Jacobi and Gauss-Seidel method. Solve the following given system of linear equation using Jacobi method. $$5x+y+z=7$$ $$x+4y+z=6$$ $$x+y+3z=5$$

Differentiate between absolute and relative error. Explain fixed point iteration method.

Fit a second-degree polynomial using least square method for: $(-1,2),(0,1),(1,2),(2,5),(3,10)$.

Find first and second derivative at $x=2$ from the following tabulated data value: $x$11.522.53$f(x)$13.375815.62527

What is numerical integration? Derive Newton-Cote's quadrature formula.

Integrate ${\int }_1^2\frac{e^x}{x}dx$ using the trapezoidal rule with $n=5$.

Solve following system of linear equation by Gauss elimination with partial pivoting. $$2x+3y+z=9$$ $$x+4y+5z=15$$ $$3x+y+2z=10$$

Use the differential equation $\frac{dy}{dx}=2x+3y$ with initial condition $y(0)=1$. Find $y(0.2)$ using the Runge-Kutta method.

Differentiate between initial value and boundary value problem. Explain solution of system of ODEs.

Explain the classification of partial differential equations by order and linearity.