Other Math Answers

The iteration method
xn+1 = 1/8[ 6xn + 3N/xn -xn^3/N], n= 0,1,2
where N is positive constant, converges to some quantity. Determine this quantity. Also find the rate of convergence of this method.

Find the solution of the difference equation yk+2 -4yk+1 +4yk =0, k=0,1,...... Also find the particular solution when y0=1 and y1=6.

Suppose fn denotes the value of f(t) at t=tn. If f(t) =t^3 then find the value of
(fn+1 -2fn +fn-1)/h^2

Take 10 figure logarithm to base 10 from x=300 to x=310 by unit increment. Calculate the first derivative of log10 x when x=310

Solve the I.V.P y'=-y +1 +1, 0<=t<=1 using R-K method of 0(h^4) 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 y(t)= t + e^-t

Obtain an approximate value of integration 0 to 1 dx/1+x^2 using composite Simpson's rule with h=0.25 and h=0.125. find also the improved value using Romberg integration.

The solution of the system of equations (1 2, 2 1) (x, y) =(4, -2) is attempted by Gauss Jacobi and Guass Seidel iteration schemes. Set up the two schemes in matrix form. Will the iteration schemes converge? Justify your an answer.

Starting with x^(0) =[1 1 1]^T, find the dominant eigenvalue and corresponding eigenvector for the matrix A= [4 -1 1, 4 -8 1, -2 1 5] using the power method.

solve the following linear system ax=b of equation with partial pivoting
x1 -x2 +3x3 =3
2x1 +x2 +4x3 =7
3x1 + 5x2 -2x3 =6
Store the multipliers and also write the pivoting vectors.