BCA Numerical Methods

Explain different types of errors in numerical computation with examples.

Apply Bisection Method to find a real root of \(x^3 - x - 1 = 0\) correct up to three decimal places.

Construct Lagrange's interpolation polynomial for the data:

Derive Newton's forward interpolation formula

Fit a straight line \(y = ax + b\) to the following data using the Least Squares Method

Apply Trapezoidal rule to evaluate a definite integral.

Differentiate between Interpolation and approximation with their significances. Derive the formula for Simpson's (3/8) composite 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 \(\frac{dy}{dx} = x + y, y(0) = 1\) using Euler's method (\(h = 0.1\)) for \(x = 0.1\).

Explain Shooting Method for boundary value problems with algorithm.