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.
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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.
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.
Show that
where μ and are the average and central
differences operators, respectively.
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.
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.
Calculate the third-degree Taylor polynomial about x0 = 0 for f(x) = (1 +x)1/2.
Use the polynomial in part (i) to approximate
.