MTH603 - Numerical Analysis

dy dx = 1 - y,y(0) = 0 is an example of Answer An ordinary differential equation A partial differential equation A polynomial equation None of the given choices

In Double integration, the interval [a, b] should be divided into [c, d) should be divided into --sub intervals of size k. --subintervals of size h and the interval Answer equal, equal equal, unequal unequal, equal unequal, unequal

The (n + 1) th difference of a polynomial of degree n is… Answer 0 Constant n +1

Let P be any real number and h be the step size of any interval. Then the relation between h and P for the backward difference is given by Answer x-x, = Ph x- x, = P x + x, = Ph (x - x,)h= P

In integrating $\int_{0}^{\frac{2}{2}} \cos x d x$ by dividing the interval into four equal parts, width of the interval should be Answer $\frac{\pi}{2}$ $\pi$ $\frac{\pi}{8}$

In fourth order Runge-Kutta method K 4 is given by Answer k4 = hf(xn th,yn + kz) k4 = hf(xn + 2h, + 2kz) None of the given choices k4 = hf(x, — h,Yn — kz)

In fourth order Runge-Kutta method k2 is given by Answer ^2-“/”“” З’Уп 3’ k2 = 45(-12.30-42)

What is the Process of finding the values outside the interval (Xo,x,) called? Answer interpolation iteration Polynomial equation extrapolation

When we apply Simpson’s 3/8 rule, the number of intervals n must be Answer Even Odd Multiple of 3 Page 177 Similarly in deriving composite Simpson’s 3/8 rule, we divide the interval of integration into n sub-intervals, where n is divisible by 3, and applying the integration formula Multiple of 8

Milne’s P-C method is a multi step method where we assume that the solution to the given initial value problem is known at past –equally spaced points. Answer 2 1 3 4 1

The truncation error in Adam’s predictor formula is …-times more than that in corrector formula Answer 10 11 12 13

Answer 10 11 12 13

Given the following data Which formula is useful in finding the interpolating polynomial? Answer Lagrange’s interpolation formula X 1 2 5 9 f(x) 2 0 30 132 Page 135 Newton’s forward difference interpolation formula Newton’s backward difference interpolation formula None of the given choices

Answer An ordinary differential equation A partial differential equation A polynomial equation None of the given choices

Answer more accurate less accurate equally accurate none of the given choices

Answer 0.250 0.500 0.125 0.625

7 8 5 3 Page 177 The Simpson’s 1/3 rule, we have used two sub-intervals of equal width. In order to get a composite formula, we shall divide the interval of integration [a, b] Into an even number

Equally spaced Not equally spaced Constant None of the above

If there are (n+1) values of y corresponding to (n+1) values of x, then we can represent the function f(x) by a polynomial of degree

Re: MTH603 Assignment 1 Solution and Discussion Assignment No. 1 MTH603 (Spring 2022) Total Marks: 20 Due Date: 8th June, 2022 DON’T MISS THESE: Important instructions before attempting the solution of this assignment: • To solve this assignment, you should have good command over 1-8 lectures. • Upload assignments properly through the LMS, No Assignment will be accepted through email. • Write your ID on the top of your solution file. Don’t use colored backgrounds in your solution files. Use Math Type or Equation Editor, etc. for mathematical symbols. You should remember that if the solution files of some students are finding the same (copied), we will reward zero marks to all those students. Make a solution by yourself and protect your work from other students, otherwise both original and copied assignments will be awarded zero marks. Also remember that you are supposed to submit your assignment in Word format, any other format like scanned images, etc. will not be accepted and be awarded zero marks Question 1 Find a real root of the equation 2x+cos⁡(x)+e^x=0 using Bisection Method using Newton Raphson Method Also compare the results and comment which of the methods performs better and which is worst. You will consider x_0=-0.6557 as a best approximation while comparing the roots. Note: In each of the above methods,you are required to perform three iterations. Spring 2022_MTH603_1.docx