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.
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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.
Take 10 figure logarithm to bases 10 from x = 300 to x = 310 by unit increment. Calculate the first derivative of log10 x when x = 310.
Show that ux = c1eax + c2e-ax is a solution of the difference equation
ux+1 - 2ux cosh .
Using finite differences, show that the data
| x | − 3 | − 2 | − 1 | 0 | 1 | 2 | 3 |
| f ( x) | 13 | 7 | 3 | 1 | 1 | 3 | 7 |
Estimate the eigenvalues of the matrix
using the Gershgorin bounds. Draw a rough sketch of the region where the eigenvalues lie.
Using the classical R-K method of o(h4) calculate approximate solution of the IVP, y' = 1− x + 4y, y(0) = 1 at x = 0.6, taking h = 0.1 and 0.2 . Use extrapolation technique to improve the accuracy.
The equation x2 + ax + b = 0 has two real roots p and q such that | p | < | q |. If we use the fixed point iteration , to find a root then to which root does it converge?