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  5. Errors in Computations.
dy/dx - = 1 - y,y(0) = 0 is an example of
L
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
MTH603 - Numerical Analysis
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
zaasmiZ
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
MTH603 - Numerical Analysis
The (n + 1) th difference of a polynomial of degree n is...
Kevin AustinK
The (n + 1) th difference of a polynomial of degree n is… Answer 0 Constant n +1
MTH603 - Numerical Analysis
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
G
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
MTH603 - Numerical Analysis
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
zaasmiZ
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 $\frac{\pi}{2}$ $\pi$ $\frac{\pi}{8}$
MTH603 - Numerical Analysis
In fourth order Runge-Kutta method K 4
zaasmiZ
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)
MTH603 - Numerical Analysis
In fourth order Runge-Kutta method k2
zaasmiZ
In fourth order Runge-Kutta method k2 is given by Answer ^2-“/”“” З’Уп 3’ k2 = 45(-12.30-42)
MTH603 - Numerical Analysis
What is the Process of finding the values outside the interval (Xo,x,) called?
zaasmiZ
What is the Process of finding the values outside the interval (Xo,x,) called? Answer interpolation iteration Polynomial equation extrapolation
MTH603 - Numerical Analysis
When we apply Simpson's 3/8 rule, the number of intervals n must be
zaasmiZ
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
MTH603 - Numerical Analysis
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.
zaasmiZ
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
MTH603 - Numerical Analysis
The truncation error in Adam's predictor formula is ....-times more than that in corrector formula
zaasmiZ
The truncation error in Adam’s predictor formula is …-times more than that in corrector formula Answer 10 11 12 13
MTH603 - Numerical Analysis
To apply Simpson's 3/8 rule, the number of intervals be
zaasmiZ
Answer 10 11 12 13
MTH603 - Numerical Analysis
Which formula is useful in finding the interpolating polynomial?
zaasmiZ
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
MTH603 - Numerical Analysis
Rate of change of any quantity with respect to another can be modeled by
zaasmiZ
Answer An ordinary differential equation A partial differential equation A polynomial equation None of the given choices
MTH603 - Numerical Analysis
Romberg's integration method is ------ than Trapezoidal and Simpson's rule.
zaasmiZ
Answer more accurate less accurate equally accurate none of the given choices
MTH603 - Numerical Analysis
In integrating f, e2* dx by dividing into eight equal parts, width of the interval should be......
zaasmiZ
Answer 0.250 0.500 0.125 0.625
MTH603 - Numerical Analysis
To apply Simpson's 1/3 rule, valid number of intervals are?
zaasmiZ
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
MTH603 - Numerical Analysis
Newton's divided difference interpolation formula is used when the values of the independent variable are
zaasmiZ
Equally spaced Not equally spaced Constant None of the above
MTH603 - Numerical Analysis
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
zaasmiZ
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
MTH603 - Numerical Analysis
MTH603 Assignment 1 Solution and Discussion
cyberianC
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
MTH603 - Numerical Analysis

Errors in Computations.

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  • W Offline
    W Offline
    waheedzaman1998
    wrote on last edited by
    #2

    If do calculation in degree for transcendental equation .what will happen ? Because in previous classes we learned that degree and Radian are interchangeable. Why focussing on Radian…? I am grateful to you sir.

    zaasmiZ 1 Reply Last reply
    0
    • W waheedzaman1998

      If do calculation in degree for transcendental equation .what will happen ? Because in previous classes we learned that degree and Radian are interchangeable. Why focussing on Radian…? I am grateful to you sir.

      zaasmiZ Offline
      zaasmiZ Offline
      zaasmi
      Cyberian's Gold
      wrote on last edited by
      #3

      @waheedzaman1998 said in Errors in Computations.:

      If do calculation in degree for transcendental equation .what will happen ? Because in previous classes we learned that degree and Radian are interchangeable. Why focussing on Radian…? I am grateful to you sir.

      Dear @waheedzaman1998,

      When we solve the transcendental equations, we take values in radian. For example consider equation x+cosx=0, here we take values in radian because we cannot take the value of a number x in degree.

      Discussion is right way to get Solution of the every assignment, Quiz and GDB.
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      • S Offline
        S Offline
        sebastine
        wrote on last edited by
        #4

        Please give me any two example which shows the data has “INHERENT ERROR”.

        zaasmiZ 1 Reply Last reply
        0
        • S sebastine

          Please give me any two example which shows the data has “INHERENT ERROR”.

          zaasmiZ Offline
          zaasmiZ Offline
          zaasmi
          Cyberian's Gold
          wrote on last edited by
          #5

          @sebastine said in Errors in Computations.:

          Please give me any two example which shows the data has “INHERENT ERROR”.

          These are the errors involve in the statement of a problem. When a problem is first analyst it may contain certain data or parameters. If the data or parameters in some way determined by physical meaurements, they will probabaly diff from exact values. For example square root 2 and pi.

          Discussion is right way to get Solution of the every assignment, Quiz and GDB.
          We are always here to discuss and Guideline, Please Don't visit Cyberian only for Solution.
          Cyberian Team always happy to facilitate to provide the idea solution. Please don't hesitate to contact us!
          [NOTE: Don't copy or replicating idea solutions.]
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          • Dream BoyD Offline
            Dream BoyD Offline
            Dream Boy
            wrote on last edited by
            #6

            Aoa sir! Again explain the example of truncating error.

            zaasmiZ 1 Reply Last reply
            0
            • Dream BoyD Dream Boy

              Aoa sir! Again explain the example of truncating error.

              zaasmiZ Offline
              zaasmiZ Offline
              zaasmi
              Cyberian's Gold
              wrote on last edited by
              #7

              @dream-boy said in Errors in Computations.:

              Aoa sir! Again explain the example of truncating error.

              Truncation Error:

              This error is caused by solving not the problem rather some approximation to it. This is usually caused by the replacement of an infinite process by a finite approximation. This error is known as truncation error.

              In the explained example of ‘‘cosx’’, when infinite series of cos x is truncated (stopped, shorten) to some ‘‘n’’ terms then further terms involved in this series is called the truncation error.

              Discussion is right way to get Solution of the every assignment, Quiz and GDB.
              We are always here to discuss and Guideline, Please Don't visit Cyberian only for Solution.
              Cyberian Team always happy to facilitate to provide the idea solution. Please don't hesitate to contact us!
              [NOTE: Don't copy or replicating idea solutions.]
              VU Handouts
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              • Vu KickV Offline
                Vu KickV Offline
                Vu Kick
                wrote on last edited by
                #8

                What is synchronous and asynchronous and what are there applications in real world. Which applications use this sort of techniques.

                zaasmiZ 1 Reply Last reply
                0
                • Vu KickV Vu Kick

                  What is synchronous and asynchronous and what are there applications in real world. Which applications use this sort of techniques.

                  zaasmiZ Offline
                  zaasmiZ Offline
                  zaasmi
                  Cyberian's Gold
                  wrote on last edited by
                  #9

                  @vu-kick said in Errors in Computations.:

                  What is synchronous and asynchronous and what are there applications in real world. Which applications use this sort of techniques.

                  The word synchronous and asynchronous are very general terms that are used in different fiels representing different phenonena. If you can please ask it more clearly that in what context you are asking. It will be good if you please mention what page of handouts, what slide of ppts or where in the lecture video of the numerical analysis you studied/heard about it. Then we’ll be able to explain it well.

                  Best wishes

                  Discussion is right way to get Solution of the every assignment, Quiz and GDB.
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                  Cyberian Team always happy to facilitate to provide the idea solution. Please don't hesitate to contact us!
                  [NOTE: Don't copy or replicating idea solutions.]
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