Numerical Methods - Unit Wise Questions

Unit 1: Solution of Nonlinear Equations
2 Questions

1. How Secant methods differs from Newton Raphson method? Derive the formula for Secant Method. Solve the equation cosx+2sinx-x2=0 using Secant method. Assume error precision is 0.01.     {2+4+4}

10 marks | Asked in Model Question

4. Define the terms true error and relative error? Write down algorithm for Horner’ method to evaluate polynomial and use the method to evaluate the polynomial 2x3 -3x2+5x-2 at x=3. {1+2+2}

5 marks | Asked in Model Question

Unit 2: Interpolation and Regression
3 Questions

2. How interpolation differs from regression? Write down algorithm and program for Lagrange interpolation.     {2+4+4}

10 marks | Asked in Model Question

5. Construct Newton’s backward difference table for the given data points and approximate the value of f(x) at x=45.

5 marks | Asked in Model Question

6. Fit the quadratic curve through the following data points and estimate the value of f(x) at x=2.

5 marks | Asked in Model Question

Unit 3: Numerical Differentiation and Integration
2 Questions

8. How can we calculate derivatives of continuous functions? Write down algorithm and program for differentiating continuous function using two point forward difference formula.

5 marks | Asked in Model Question

9. Find following integral using composite trapezoidal rule using 2 segments (k=2) and 4 segments (k=4).

5 marks | Asked in Model Question

Unit 4: Solving System of Linear Equations
2 Questions

3. Explain the working of Jacobi Iteration method? Solve the following system of equations using the method. Assume error precision is 0.01. Compare Jacobi Iteration method with Gauss-Seidel method.     {4+4+2}

5x-2y+3z=-1

-3x+9y+z=2

2x-y-7z=-3

10 marks | Asked in Model Question

7. Derive formula for the Doolittle LU decomposition matrix factorization method.

5 marks | Asked in Model Question

Unit 5: Solution of Ordinary Differential Equations
2 Questions

10. Approximate the solution of y’=2x+y, y(0)=1 using Euler’s method with step size of 0.1. Approximate the value of y(0.4).

5 marks | Asked in Model Question

12. How boundary value problems differs from initial value problems? Discuss shooting method for solving boundary value problem.

5 marks | Asked in Model Question

Unit 6: Solution of Partial Differential Equations
1 Questions

11. Solve the Poisson’s equation  with f = 2 on boundary by assuming square domain  and h=1.

5 marks | Asked in Model Question