What is the cube root of 1468 to 3 decimal places?
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Engineering Maths · all questionsNumerical Methods
Numerical Methods
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Torque exerted on a flywheel over a cycle is listed in the table. Flywheel energy (in J per unit cycle) using Simpson's rule is
| Angle (degree) | 0 | 60 | 120 | 180 | 240 | 300 | 360 |
| Torque (Nm) | 0 | 1066 | -323 | 0 | 323 | -355 | 0 |
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Roots of the algebraic equation x3 + x2 + x + 1 = 0 are
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In the Newton-Raphson method, an initial guess of x0 = 2 is made and the sequence x0, x1, x2 ... is obtained for the function 0.75x3 - 2x2 - 2x + 4 = 0
Consider the statements
I. x3 = 0.
II. The method converges to a solution in a finite number of iterations.
Which of the following is TRUE?
Consider the statements
I. x3 = 0.
II. The method converges to a solution in a finite number of iterations.
Which of the following is TRUE?
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While numerically solving the differential equation using Euler's predictor-corrector (improved Euler-Cauchy) with a step size of 0.2, the value of y after the first step is
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The Newton-Raphson iteration can be used to compute the
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When the Newton-Raphson method is applied to solve the equation f(x) = x3 + 2x - 1 = 0, the solution at the end of the first iteration with the initial guess value as x0 = 1.2 is
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The matrix \left[ {\text{A}} \right] = \left[ {\begin{array}{*{20}{c}}
2&1 \\
4&{ - 1}
\end{array}} \right] is decomposed into a product of a lower triangular matrix x[L] and an
upper triangular matrix [U]. The properly decomposed [L] and [U] matrices respectively are
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Consider a differential equation with the initial condition y(0) = 0. Using Euler's first order method with a step size of 0.1, the value of y(0.3) is
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Consider an ordinary differential equation If x = x0 at t = 0, the increment in x calculated using Runge-Kutta fourth order multistep method with a step size of Δt = 0.2 is
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Newton-Raphson method is used to compute a root of the equation x2 - 13 = 0 with 3.5 as the initial value. The approximation after one iteration is
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Identify the Newton-Raphson iteration scheme for finding the square root of 2.
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If a continuous function f(x) does not have a root in the interval [a, b], then which one of the following statements is TRUE?
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Consider p(s) = s3 + a2s2 + a1s + a0 with all real coefficients. It is known that it is derivative p'(s) has no real roots. The number of real roots of p(s) is
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The differential equation is discretised using Euler's numerical integration method with a time step ΔT > 0. What is the maximum permissible value of ΔT to ensure stability of the solution of the corresponding discrete time equation?
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Match the correct pairs
| Numerical Integration Scheme | Order of Fitting Polynomial |
| P. Simpson's 3/8 Rule | 1. First |
| Q. Trapezoidal Rule | 2. Second |
| R. Simpson's 1/3 Rule | 3. Third |
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The minimum number of equal length subintervals needed to approximate to an accuracy of at least using the trapezoidal rule is
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Consider the series obtained from the Newton-Raphson method. The series converges to
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The value of the function f(x) is given at n distinct values of x and its value is to be interpolated at the point x⋆, using all the n points. The estimate is obtained first by the Lagrange polynomial, denoted by and then by the Newton polynomial, denoted by . Which one of the following statements is correct?
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The extremum (minimum or maximum) point of a function f(x) is to be determined by solving using the Newton-Raphson method. Let f(x) = x3 - 6x and x0 = 1 be the initial guess of x. The value of x after two iterations (x2) is
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