Explain different types of errors in numerical computation with examples.
Apply Bisection Method to find a real root of x³ − x − 1 = 0 correct up to three decimal places.
Construct Lagrange’s interpolation polynomial for the data:
| X | 1 | 2 | 4 |
| Y | 1 | 4 | 16 |
Derive Newton’s forward interpolation formula.
Solve the following set of linear equations using Gauss Jordan method:
x + y + z = 6
2x + 3y + z = 10
x + 2y + 3z = 13
Solve dx/dy=x+y, y(0) = 1 using Euler’s method (h = 0.1) for x = 0.1.
Apply Trapezoidal rule to evaluate a definite integral.
Attempt any TWO questions
[2x10=20]Explain Shooting Method for boundary value problems with algorithm.
Fit a straight line y = ax + b to the following data using the Least Squares Method:
| x | 1 | 2 | 3 | 4 |
| y | 2 | 5 | 7 | 8 |
Differentiate between Interpolation and approximation with their significances.
Derive the formula for Simpson’s (3/8) composite formula.