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Math
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
(fn+1 -2fn +fn-1)/h^2
For the table of values f(x) =xe^x given by
x f(x)
1.8 10.8894
1.9 12.7032
2.0 14.7781
2.1 17.1489
2.2 19.8550
Find f"(2.0) using the central difference formula of 0(h^2) fir h=0.1 and h=0.2. Calculate T.E. and actual error.
x f(x)
1.8 10.8894
1.9 12.7032
2.0 14.7781
2.1 17.1489
2.2 19.8550
Find f"(2.0) using the central difference formula of 0(h^2) fir h=0.1 and h=0.2. Calculate T.E. and actual error.
Math
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
The position f(x) of a particle moving in a line at various times xk is given in the following table. Estimate the velocity and acceleration of the particle at x=1.2
x f(x)
1.0 2.72
1.2 3.32
1.4 4.06
1.6 4.96
1.8 6.05
2.0 7.39
2.2 9.02
x f(x)
1.0 2.72
1.2 3.32
1.4 4.06
1.6 4.96
1.8 6.05
2.0 7.39
2.2 9.02
Math
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
Consider the following data
x f(x)
1.0 0.7651977
1.3 0.6200860
1.9 0.2818186
2.2 0.1103623
Use Stirling's formula to approximate f(1.5) with x0= 1.6
x f(x)
1.0 0.7651977
1.3 0.6200860
1.9 0.2818186
2.2 0.1103623
Use Stirling's formula to approximate f(1.5) with x0= 1.6
Math
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.
Math
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.
Math
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.
