Numerical Analysis and Computational Physics — DU B.Sc. (Hons) Physics Previous Year Question Papers

Semester H-Semester (GE paper) a) Evaluate the sum S = `/g + `/5 + `/7 to 4 significant digits and find its absolute and b) relative error. From the following table, find the. area bounded by the curve and the x-axis from x = 7.47tox=7.52usingSimpson's[/3rule. c) Given ¥ = % -y with y(0) = 1. Find the value of y(1) using Euler's method with fr = 0.5. d) Write the formula of Secant method for solving algebraic and transcendental equations. Explain graphically. Given f(x) = cos(%) 7I e) Construct the Taylor series approximation of order 5 at # = ;. D Prove that A3yo = y3 - 3y2 + 3yi -yo where A3 is the third order forward difference for data points (#o,yo); (Xi,yi); (X2, y2) and (X3,y3). a) Using Bisection method, find a real root of the following equation in the interval [2, 3], correct to four decimal places. (8) •,ap b) Derive the expression of error associated with Newton-Raphson method of solving algebraic and transcendental equations. Under what conditions can the method fall to converge. (7) a) Find the best values of a and b so that y = orb fits the data given in the table. X 10 20 30 40' 50 b) Values of # (in degrees) and sin(x) are given in the following table: # (in degrees) sine) Determine the value of sin 38° using Newton's interpolation formula. (7) a) A rod is rotating in plane about one of its ends. The angle G (in radians) at different times i (seconds) are given below: (8) Find its angular velocity and angular acceleration when f = 0.6 seconds. b) Approximate the value of /oL G-# dr using Trapezoidal rule with n = 10 and verify the theoretical error bound holds for the same. (7) a) Use Runge-Kutta fourth order method to find y(1.2) and y(1.4) given that dy 3x+y b) For the values of x and y given below, find the value of y at x = 10 using Lagrange interpolation. (7)