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A

Section A: Long Answer Questions

Attempt any TWO questions.

3 questions·10 marks each
1long10 marks

Explain the fourth-order Runge-Kutta method for solving ordinary differential equations. Solve dy/dx = x + y, y(0) = 1 to find y(0.2) taking h = 0.1.

oderunge-kutta
2long10 marks

Derive the Newton-Raphson method for solving a non-linear equation and discuss its convergence. Find a root of x^3 - 2x - 5 = 0 correct to four decimal places.

nonlinearnewton
3long10 marks

What is curve fitting? Explain the least squares method to fit a straight line y = a + bx to a given set of data points.

regression
B

Section B: Short Answer Questions

Attempt any EIGHT questions.

9 questions·5 marks each
4short5 marks

Explain numerical differentiation using forward and backward difference formulae.

differentiation
5short5 marks

Explain Euler's method to solve an ordinary differential equation with an example.

odeeuler
6short5 marks

Differentiate between the Gauss elimination and Gauss-Jordan methods.

linear-systemsgauss-jordan
7short5 marks

Explain Newton's divided difference interpolation formula.

interpolationdivided-difference
8short5 marks

Explain the power method for finding the largest eigenvalue of a matrix.

eigenvalue
9short5 marks

Fit a second-degree parabola y = a + bx + cx^2 to a set of data using the least squares principle.

regression
10short5 marks

Define absolute, relative and percentage errors. Explain the sources of errors in numerical computation.

errors
11short5 marks

Explain the secant method for finding the root of an equation and compare it with the Newton-Raphson method.

nonlinearsecant
12short5 marks

Describe the false position (regula falsi) method with its geometric interpretation.

nonlinearfalse-position