Numerical Differentiation and Integration

The second derivative of the Newton’s forward differentiation is _________.

• y ” = (1/h2)* {D2y0 – D3y0 + (11/12) D4y0 ……….}

• y ” = (1/h2)* {D2y0 + D3y0 + (11/12) D4y0 ……….}

• y ” = (1/h)* {D2y0 + D3y0 + (11/12) D4y0 ……….}

• y ” = (1/h)* {D2y0 – D3y0 + (11/12) D4y0 ……….}

Simpson’s one-third rule on numerical integration is called a _________ formula.

• closed

• opened

• semi closed

• semi opened

Numerical evaluation of a definite integral is called _________.

• Integration

• Differentiation

• Interpolation

• Triangularization

The second derivative of the Newton’s backward differentiation is _________.

• y ” = (1/h2)* {D2y0 + D3y0 + (11/12) D4y0 ……….}

• y ” = (1/h2)* {D2y0 – D3y0 + (11/12) D4y0 ……….}

• y ” = (1/h)* {D2y0 + D3y0 + (11/12) D4y0 ……….}

• y ” = (1/h)* {D2y0 – D3y0 + (11/12) D4y0 ………..}

The order of error in Trapezoidal rule is _________.

• h

• h³

• h²

• h⁴

The order of error in Simpson’s rule is _________.

• h

• h³

• h²

• h⁴

Simpson’s ⅜ rule can be applied only if the number of sub interval is in _________.

• Equal

• even

• multiple of three

• unequal

By putting n = 2 in Newton cote’s formula we get _________ rule.

• Simpson’s 1/3

• Simpson’s ⅜

• Trapezoidal

• Romberg

The Newton Cote’s formula is also known as _________ formula.

• Simpson’s 1/3

• Simpson’s 3/8

• Trapezoidal

• Quadrature

By putting n = 3 in Newton cote’s formula we get _________ rule.

• Simpson’s 1/3

• Simpson’s ⅜

• Trapezoidal

• Romberg