Numerical Method 2066

Attempt all questions:

1. Define the fixed-point iteration method. Given the function f(x) = x² − 2x − 3 = 0, rearrange the function in such a way that the iteration method converses to its roots. (2+3+3)

2. What do you mean by interpolation problem? Define divided difference table and construct the table from the following data set. (2+2+4)

OR

Find the least squares line that fits the following data.

What do you mean by linear least square approximation?

3. Derive the composite formula for the trapezoidal rule with its geometrical figure. Evaluate dx using this rule with n=5, upto 6 decimal places.(4 + 4)

6. Derive a difference equation to represent a Poison’s equation. Solve the Poison’s equation ∇² f = 2x²y² over the domain 0 ≤ x ≤ 3, 0 ≤ y ≤ 3 with f = 0 on the boundary and h = 1.(3 + 5)

7. Define ordinary differential equation of the first order. What do you mean by initial value problem? Find by Taylor’s series method, the values of y at x = 0.1 and x = 0.2 to find places of decimal form

(2 + 6)