Engineering Mat...

Using the trapezoidal rule, and dividing the interval of integration into three equal subintervals, the definite integral \(\mathop \smallint \limits_{ - 1}^{ + 1} \left| x \right|dx\) is _____

Match the application to appropriate numerical method.

1) P1—M3, P2—M2, P3—M4, P4—M1

2) P1—M3, P2—M1, P3—M4, P4—M2

3) P1—M4, P2—M1, P3—M3, P4—M2

4) P1—M2, P2—M1, P3—M3, P4—M4

The root of the function f(x) = x³ + x – 1 obtained after first iteration on application of Newton-Raphson scheme using an initial guess of x₀ = 1 is

Only one of the real roots of f(x) lies in the interval 2 ≤ x ≤ 4 and bisection method is used to find its value. The minimum number of iterations required to achieve an accuracy of 0.2% is ______

Consider the first order initial value problem y’ + y = 0, y(0) = 1 for x = 0.1, the solution obtained using a single iteration  of the third order Runge Kutta method with step-size h = 0.1 is _________.

The equation 2x³ + 5x - 12 = 0 is to be solved numerically using Newton-Raphson method. If x_{k + 1} is 2% more than x_k (where k represents the iteration level), then identify the correct option.

The evaluation of the definite integral \(\mathop \smallint \nolimits_{ - 1}^{1.4} x\left| x \right|dx\) by using Simpson’s 1/3^rd (one –third) rule with step size h = 0.6 yields

In the differential equation \(\frac{{dy}}{{dx}} = \sqrt {{x^2} + {y^2}} ,y\left( 1 \right) = 2\) is solved using the Euler’s method with step size h = 0.1, then y₂ is equal to (round off to 2 places of decimal)

The root of equation 2x – log x = 7 by regula falsi method correct to three places of decimal is –

In the solution of the following set of linear equation by Gauss elimination using partial pivoting the pivots for the elimination of x and y are _______ respectively

x + 4y – z = -5

x + y – 6z = -12