This download link is referred from the post: GTU B.Tech 2020 Winter Question Papers || Gujarat Technological University
Time: 02:30 PM TO 04:30 PM
Instructions:
--- Content provided by FirstRanker.com ---
Attempt any FOUR questions out of EIGHT questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
GUJARAT TECHNOLOGICAL UNIVERSITY
BE- SEMESTER-IV (NEW) EXAMINATION - WINTER 2020
--- Content provided by FirstRanker.com ---
Subject Code: 2140105Subject Name: Numerical Methods
Date: 09/02/2021
Total Marks: 56
| Question | Marks |
|---|---|
| Q.1 (a) Define and name the methods to solve differential equations. | 03 |
| (b) Implement bisection method to solve x3-3x-5=0 upto fourth approximation. | 04 |
| (c) Describe the fitting of y = aex for the data: --- Content provided by FirstRanker.com --- X 0 2 4y 5.012 10 31.62 | 07 |
| Q.2 (a) State the formulae for Newton's backward interpolation methods. Specify the methods used for unequal intervals | 03 |
| (b) Using the Lagrange’s formula find the polynomial which fits into the data below: X 0 1 5 y 2 12 147 | 04 |
| (c) Obtain cubic spline for every subinterval from the following data: X 0 3 8 --- Content provided by FirstRanker.com --- y 1 2 3 | 07 |
| Q.3 (a) Use Gauss elimination solve x+2y+z=8, 2x+3y+4z=20, 4x+3y+2z=16. | 03 |
| (b) Use Trapezoidal rule to evaluate ∫31 dx/x taking 4 subintervals. | 04 |
| (c) Describe the Newton Raphson method in brief and solve ex =5x | 07 |
| Q.4 (a) Use Gauss Jordan method to solve 10x+y+z=12, x+10y+z=12, x+y+10z=12. | 03 |
| (b) Use Simpson's 3/8 rule to evaluate, ∫60 dx | 04 |
| (c) Describe Secant method and use it to solve x2 —5x+1=0 in (0,1). | 07 |
| Q.5 (a) State the Gauss seidel method for laplace equation | 03 |
| (b) Solve heat equation ut=uxx, u(0,t)=0, u(1,t)=t. with k=1 and h=1. | 04 |
| (c) State the Taylor's method and solve equation, dy/dx = y - 2x/y, y(0)=1. | 07 |
| Q.6 (a) State the finite difference quotients for first and second order derivatives. | 03 |
| (b) Solve y''+y+1=0 with y(0)=0, y(1)=0, Using h=0.5 implement finite difference approach. | 04 |
| (c) State the Picard's formula and solve the equation for x=0.2, dy/dx = x2 + y2, y(0)=1. | 07 |
| Q.7 (a) Discuss the difference between finite difference and finite element approach | 03 |
| (b) Describe the Rayleigh Ritz method in brief. | 04 |
| (c) Solve using Runge Kutta 4th order method dy/dx = x+y, y(0)=1 using h=0.05 for y(0.1). | 07 |
| Q.8 (a) Discuss the shooting approach for boundary value problems. | 03 |
| (b) Describe the Galerkin approach in brief. | 04 |
| (c) Solve using the equation using Galerkin approach, y''+y=-x, 0<x<1 and y(0)=y(1)=0 | 07 |
This download link is referred from the post: GTU B.Tech 2020 Winter Question Papers || Gujarat Technological University
--- Content provided by FirstRanker.com ---