FirstRanker Logo

FirstRanker.com - FirstRanker's Choice is a hub of Question Papers & Study Materials for B-Tech, B.E, M-Tech, MCA, M.Sc, MBBS, BDS, MBA, B.Sc, Degree, B.Sc Nursing, B-Pharmacy, D-Pharmacy, MD, Medical, Dental, Engineering students. All services of FirstRanker.com are FREE

📱

Get the MBBS Question Bank Android App

Access previous years' papers, solved question papers, notes, and more on the go!

Install From Play Store

Download GTU B.Tech 2020 Summer 3rd Sem 3130107 Partial Differential Equations And Numerical Methods Question Paper

Download GTU (Gujarat Technological University Ahmedabad) B.Tech/BE (Bachelor of Technology/ Bachelor of Engineering) 2020 Summer 3rd Sem 3130107 Partial Differential Equations And Numerical Methods Previous Question Paper

This post was last modified on 04 March 2021

This download link is referred from the post: GTU BE 2020 Summer Question Papers || Gujarat Technological University


Envlmnt No.

Subject Code: 3130107

GUJARAT TECHNOLOGICAL UNIVERSITY

--- Content provided by FirstRanker.com ---

BE - SEMESTER- IIl EXAMINATION - SUMMER 2020

Subject Name: Partial Differential Equations and Numerical Methods

Time: 02:30 PM TO 05:00 PM Date:27/10/2020 Total Marks: 70

Instructions:

  1. Attempt all questions.
  2. --- Content provided by FirstRanker.com ---

  3. Make suitable assumptions wherever necessary.
  4. Figures to the right indicate full marks.

Q1

  1. Use Iteration method to find the real root of the equation x4 + x —1 = 0 correct to six decimal places starting with x0 =1. [03]
  2. Use Bisection method to find the real root of the equation x —cos x = 0 correct upto four decimal places. [04]
  3. --- Content provided by FirstRanker.com ---

  4. Explain the Newton-Raphson method briefly. Also find an iterative formula for √N and hence find √7 correct to three decimal places. [07]

Q2

  1. Evaluate ∫01 e-x2 dx by Simpson’s-1/3 rule with n=10 and estimate the error. [03]
  2. Solve the following linear system of equations by Gauss elimination method. [04]
    6x+8y+2z=-7

    --- Content provided by FirstRanker.com ---

    3x+5y+2z=8
    6x+2y+8z=26
  3. Compute cosh (0.56) using Newton’s forward-difference formula and also estimate the error for the following table. [07]
    x 0.5 0.6 0.7 0.8
    f(x) 1.127626 1.185465 1.255169 1.337435

    OR
  4. --- Content provided by FirstRanker.com ---

  1. The speed, v meters per second, of a car, t seconds after it starts, is show in the following table. [07]
    t 0 12 24 36 48 60 72 84 96 108 120
    v 0 3.60 10.08 18.90 21.60 18.54 10.26 4.50 4.5 5.4 9.0

    Using Simpson’s ⅓ rule, find the distance travelled by the car in 2 minutes.

Q3

  1. Use Trapezoidal rule to evaluate ∫01 x3 dx using five subintervals. [03]
  2. --- Content provided by FirstRanker.com ---

  3. Check whether the following system is diagonally dominant or not. If not, rearrange the system and solve it using Gauss-Seidel method. [04]
    8x-3y+2z=20
    4x-11y—-z=33
    6x—-3y+12z=35
  4. Explain Euler’s method briefly and apply it to the following initial value problem by choosing h =0.2 and hence obtain y(1.0). dy/dx =x+y, y(0)=0. Also determine the error by deriving it analytical solution. [07]

    --- Content provided by FirstRanker.com ---

    OR
  1. Use Fourth order method to find the approximate value of y(0.2) given that dy/dx =x+y, y(0)=1. [07]

Q4

  1. Find the Lagrange Interpolating polynomial from the following data [03]
    X 0 1 4 5
    f(x) 1 3 24 39
  2. --- Content provided by FirstRanker.com ---

  3. Derive Secant iterative method from the Newton-Raphson method and use it to find the root of the equation cosx —xex = 0 correct to four decimal places. [04]
  4. Solve (x —yz)p+(y —xz)q=z2 —xy. [07]

Q.5

  1. Solve ∂2z / ∂x2 +z =0 given that when x=0, z=ey and ∂z/∂x =1. [03]
  2. Obtain the solution of following one-dimensional Wave equation together with following initial and boundary conditions by the method of separation of variables. [04]

    --- Content provided by FirstRanker.com ---

    2u / ∂t2 = ∂2u / ∂x2
    u(0,t)=u(l,t)=0 ∀t>0
    u(x,0)= f(x) for 0 < x < l
    ut(x,0)=g(x) for 0 < x < 1
    OR
  3. --- Content provided by FirstRanker.com ---

  1. Solve pr—qz=z2 +(x+y). [07]

Q.5

  1. Solve ∂2z / ∂x2∂y = x2 +y2 +1 [03]
  2. Obtain the solution of following one-dimensional heat equation with insulated sides by the method of separation of variables. [04]
    ∂u / ∂t = ∂2u / ∂x2

    --- Content provided by FirstRanker.com ---

    u(0,t)=u(l,t)=0 ∀t>0
    u(x,0)= f(x) for 0 < x < l
  3. Solve p2-q2 =x-y [07]

Q.5

--- Content provided by FirstRanker.com ---

  1. Solve the given equation ∂u/∂t =2 ∂2u/∂x2 +u given that u(x,0) =6e-3x. [03]
  2. Obtain the solution of following one-dimensional heat equation with insulated ends by the method of separation of variables. [04]
    ∂u / ∂t = ∂2u / ∂x2
    ux(0,t)=ux(l,t)=0 ∀t>0
    u(x,0)= f(x) for 0 < x < l

    --- Content provided by FirstRanker.com ---

    OR
  1. Solve (z2(p2+q2 + 1) = 1 [07]

Q.5

  1. Using method least squares, find the best fit straight line for the following data. [03]
    X 1 2 3 4 5
    y 1 3 5 6 5
  2. --- Content provided by FirstRanker.com ---

  3. Obtain the solution following two-dimensional Laplace equation. [04]
    uxx+uyy =0
    u(0,y) = u(a,y) = u(x,0)= 0
    u(x,0)= f(x)

FirstRanker.com

--- Content provided by FirstRanker.com ---



This download link is referred from the post: GTU BE 2020 Summer Question Papers || Gujarat Technological University

--- Content provided by FirstRanker.com ---