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  5. In fourth order Runge-Kutta method k2
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

In fourth order Runge-Kutta method k2

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runge-kutta method k2in fourth ordermth603mth603 final term mcqsmth603 final term preparation
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  • zaasmiZ Offline
    zaasmiZ Offline
    zaasmi
    Cyberian's Gold
    wrote on last edited by
    #1

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

    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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    zaasmiZ 1 Reply Last reply
    0
    • zaasmiZ zaasmi

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

      zaasmiZ Offline
      zaasmiZ Offline
      zaasmi
      Cyberian's Gold
      wrote on last edited by zaasmi
      #2

      @zaasmi said in In fourth order Runge-Kutta method k2:

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

      In the fourth-order Runge-Kutta method,  is computed using the following formula:

      
      k_2 = h \cdot f\left( t_n + \frac{h}{2}, y_n + \frac{k_1}{2} \right)

      where:

      •	  h  is the step size
•	  t_n  is the current value of the
•	  y_n  is the current value of the dependent variable,
•	  k_1 = h \cdot f(t_n, y_n)  is the first slope.

      The formula you provided seems to be incorrect or misformatted. If you have specific terms or a function f(t, y) , please clarify or correct the notation so I can provide the accurate calculation for  in your context.

      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
      Quiz Copy Solution
      Mid and Final Past Papers
      Live Chat

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