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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Find the largest real root α of by f ( x) = x 6 − x − 1 = 0 lying between 1 and 2. Perform three iterations by
i) bisection method
ii) secant method ( x0 = 2, x1 = 1) .
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.
Using the following table of values, find approximately by Simpson’s rule, the arc length of the graph between the points (1 , 1) and
| x | 1 | 2 | 3 | 4 | 5 |
| 1.414 | 1.031 | 1.007 | 1.002 | 1.001 |
Calculate the third-degree Taylor polynomial about x0 = 0 for f(x) = (1 +x)1/2.
For the linear system of equations
set up the Gauss-Jacobi and Gauss-Seidal iteration schemes in matrix form. Also check the convergence of the two schemes.
Find by Newton’s method the roots of the following equations correct to three places of decimals
i) x log10 x = 4.772393 near x = 6
ii) f (x) = x − 2 sin x near x = 2
A table of values is to be constructed for the function f (x) given by in the interval [1, 4] with equal step length. Determine the spacing h such that quadratic interpolation gives result with accuracy 1x10-6.