Use modified Euler’s method to find the approximate solution of IVP
y' = 2xy, y(1) = 1 at x = 1.5 with h = 0.1
If the exact solution is y(x) = ex2-1, find the error.
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The function f (x) = ln(1+ x) is to be tabulated at equispaced points in the interval [2, 3] using linear interpolation. Find the largest step size h that can be used so that
the error < 5 x 10-4 in magnitude.
The position f (x) of a particle moving in a line at various times xk is given in the following table. Estimate the velocity and acceleration of the particle at x = 1.2.
| x | 1.0 | 1.2 | 1.4 | 1.6 | 1.8 | 2.0 | 2.2 |
| f(x) | 2.72 | 3.32 | 4.06 | 4.96 | 6.05 | 7.39 | 9.02 |
Find the dominant eigenvalue and the corresponding eigenvector for the matrix
using five iterations of the power method and taking y(10) = [111]T as the initial vector.
Solve x3 − 9x + 1 = 0 for the root lying between 2 and 4 by the method of false position. Perform two iterations
Find the inverse of the matrix
using Gauss Jordan method.
Using of x0 = −2 as an initial approximation find an approximation to one of the zeros p(x) = 2x4 − 3x2 + 3x − 4 by using Birge-Vieta method. Perform two iterations.
Solve the system of equations
0.6x + 0.8y + 0.1z = 1
1.1x + 0.4y + 0.3z = 0.2
x + y + 2z = 0.5
by LU decomposition method and find the inverse of the coefficient matrix