BCS-054 : COMPUTER ORIENTED NUMERICAL TECHNIQUES (Top 10 Most Important Questions)

1. Solve the following system of linear equations using Gauss Elimination method :

4x – 5y + z = 2
2x + y – 2z = 7
x + 4y + z = 5

2.Solve the following system of equations by using Gauss-Seidel iteration method (perform two iterations) :

8x – 3y + 2z = 20
6x + 3y + 12z = 35
4x + 11y – z = 33

3. Determine the value of 12 by NewtonRaphson method (perform 3 iterations), taking 0 x = 3.5, as initial estimate.

4. Verify the relation (1 )(1 ) 1 +∆ −∇ = , where ∆ and ∇ are forward and backward differencing operators, respectively.

5. Find the first positive root of the equation x 3 + x 2 – 10 = 0 by Regula-Falsi method. Show two iterations

6. Explain the formula for Trapezoidal rule with the help of a diagram. Also find the approximate value of I =   1 0 1 x dx using Trapezoidal rule

7. Write the Newton’s backward difference formula for evaluating dx dy .

8. Derive the formula of Trapezoidal rule using a diagram.

9. Use fourth order classical Runge-Kutta method to solve the initial value problem 2 u tu   2 with u0 1   and h  0.2 on the interval [0,1].

10. Using the Gauss-Seidel iterative method, solve the following system of linear equations :

2x + y = 7
x + 4y = 14

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