List of top Mathematics Questions on Numerical Methods

Given \[ \int_{0}^{3} f(x)\,dx=\int_{0}^{3}(4x^2-1)\,dx \] is approximated using Simpson's \(\frac{1}{3}\) rule with \(3\) subintervals and gives \(f(0)+a+f(3)\), then \(a\) is

How many minimum number of iterations are required to get an accuracy of \(0.001\) for the interval \([1,3]\) in the bisection method?

A multistep method used to solve differential equations is

If \(x_0=1.2\) is the initial guess of the solution of \(x^3+2x-1=0\), then the \(1^{\text{st}}\) iteration solution \(x_1=\)

The iterative formula for finding \(2^{\frac{1}{5}}\) using Newton-Raphson method is

A multistep method for solving a differential equation numerically among the following is

Given \[ \int_{0}^{3} f(x)\,dx=\int_{0}^{3}(4x^2-1)\,dx \] is approximated using Simpson's \(\frac{1}{3}\) rule with \(3\) subintervals and gives \(f(0)+a+f(3)\), then \(a\) is

How many minimum number of iterations are required to get an accuracy of \(0.001\) for the interval \([1,3]\) in the bisection method?

If \(x_0=1.2\) is the initial guess of the solution of \(x^3+2x-1=0\), then the \(1^{\text{st}}\) iteration solution \(x_1=\)

A multistep method used to solve differential equations is

A multistep method for solving a differential equation numerically among the following is

The iterative formula for finding \(2^{\frac{1}{5}}\) using Newton-Raphson method is

The solution of $\frac{dy}{dx} - y - 2x + x^2 = 0$, $y(0) = 1$ at $x = 0.2$ using Euler's method is:

By assuming that the solution to the equation $x^4 - x - 10 = 0$ lies between $x = 1.8$ and $x = 2$, then the next approximate solution by Regula-falsi method is (Take $f(1.8) = -1.3024$):

Given \( x_0 \neq 0 \), if the iteration formula \( x_{n+1} = \frac{1}{2}\left( -\frac{7}{x_n} + x_n \right) \), \( n \geq 0 \) is used to find the root of \( f(x) = 0 \), then \( f(x) = \)

The solution of $\frac{dy}{dx} - y - 2x + x^2 = 0$, $y(0) = 1$ at $x = 0.2$ using Euler's method is:

By assuming that the solution to the equation $x^4 - x - 10 = 0$ lies between $x = 1.8$ and $x = 2$, then the next approximate solution by Regula-falsi method is (Take $f(1.8) = -1.3024$):

Given \( x_0 \neq 0 \), if the iteration formula \( x_{n+1} = \frac{1}{2}\left( -\frac{7}{x_n} + x_n \right) \), \( n \geq 0 \) is used to find the root of \( f(x) = 0 \), then \( f(x) = \)

To find the root of the equation $f(x) \equiv e^{-x} - x = 0$, the Newton-Raphson method is used. If the initial guess for the root is 1, then the estimate of the root after first iteration is _______}

The iterative formula for finding the approximate root of $f(x) = 0$ using Newton-Raphson method is:

For a Binomial distribution, mean is \(15\) and variance is \(6\). If \[ P(X\ge2) = 1-\left(\frac25\right)^{25}k, \] then \(k=\)

Approximate positive root of the equation \[ x^2-7x+9=0 \] using Newton-Raphson method with initial guess \(x_0=2\).

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?