Starting with find the dominant eigenvalue and corresponding eigenvector for the matrix
using the power method.
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Obtain an approximate value of using composite Simpson’s rule with h = 0.25 and
h = 0.125 Find also the improved value using Romberg integration.
Suppose n f denotes the value of then find the value of
Using x o= 0 find an approximation to one of the zeros of x³-4x+1=0 by using Birge-Vieta Method. Perform two iterations.
Find an approximate value of the positive real root of xe x= 1 using graphical method. Use this value to find the positive real root of xex = 1 correct to three decimal places by fixed point iteration method.
Using sin( 0.1) = 0.09983 and sin( 0.2) = 0.19867 , find an approximate value of sin( 0.15) by using Lagrange interpolation. Obtain a bound on the truncation error.
Using Maclaurin’s expansion for sin x , find the approximate value of 4 sin with the error bound 5 10 -5
Solve the using R-K method of 0(h4 ) with
h = 0.1 and obtain the value of y(0.2) . Also find the error at t = 0.2 , if the exact solution is