List of top Mathematics Questions on Numerical Methods asked in CPET

What is the approximate value of the integral \(\int_0^1(x+x^2)\,dx\), when Simpson's 1/3-rd rule is applied with 2 sub-intervals?

Which one of the following statements about the central difference and averaging operators is correct?

For what value(s) of the constants \(a\), \(b\) and \(c\) is the quadrature formula \[\int_{-1}^1 f(x)\,dx \approx af(-1)+bf(0)+cf(1)\] exact for polynomials of degree up to 3?

Regula Falsi method is used to find a root of the equation \(f(x)=x^3-x-1\) by choosing the initial guesses \(x_0=1\) and \(x_1=2\). What would be the value of the next iteration (i.e. \(x_3\)) up to two decimal places?

Using Newton's divided difference method, the second divided difference for the function values f(1)=2, f(2)=3, f(4)=7 is approximately equal to ____.

Which of the following statements is/are true?
(I) Gauss-Seidel method for solving a linear system converges faster than the Gauss-Jacobi method.
(II) In the Gauss-Jordan method for solving a linear system, the coefficient matrix is transformed into an upper triangular matrix.

Using Lagrange interpolation with the following function values, find the approximate value of \(f(2)\).

x	0	1	3
f(x)	1	2	4