Quantitative Methods Answers

Q. How to control size of h in Runge Kutta Fehlberg Method?

Q. How to control error in Runge Kutta Fehlberg Method?

Q. Write and solve an example of Runge Kutta Fehlberg Method.

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.

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

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

Write down only one application of Runge Kutta Method to solve some real world problem

Write down Runge Kutta Fehlberg Method(Error Control)

using sin(0.1)= 0.09983 and sin(0.2)= 0.19867, find an approximate value of sin(0.15) by using Lagrange's interpolation. Obtain a bound on the truncation error.

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