Numerical Method 2072

Attempt all questions:

1. What are the sources of errors? Discuss various types of errors. Find the roots of the equation x² + 5.6x − 10= 0 by trial and error method up to 4 significant digits. (1+3+4)

2. Describe Newton’s method and its convergence. Find the root of equation f(x) = e^x− 4x² = 0      using Newton method up to 5 decimal places. (4+4)

3. What do you mean by interpolation and approximation? Use Lagrange interpolation to estimate the value of f(0.6) from the following table of values. (2+6)

4. Using Newton’s divided difference interpolating polynomial estimate the value of f(x) at x = 2.25 for the function defined as

5. Write algorithm for Gauss- Seidel method for solving the system of linear equations. Also solve the following system of linear equations using that method. (4+4)

        10x₁ + x₂ + x₃ = 12

        x₁ + 10x₂ - x₃ = 10

        x₁ - 2x₂ + 10x = 9

6. What do you understand by the partial differential equation? Illustrate it with practical example and derive difference equation. (8)

OR

Find the solution of following differential equations using Taylor series method.

6. What do you understand by the partial differential equation? Illustrate it with practical example and derive difference equation. (8)

OR

Find the solution of following differential equations using Taylor series method.

7. Write an algorithm and program for computer to obtain the solution of differential equation using Runge-Kutta Method. {5+7)